Definitely yes-but not like you might think.

"Is the voice of God something you can hear?"  This question presumes that God has a voice. Does God have a voice? Let us travel back in time several thousand years to the base of Mount Sinai. In Exodus 19:9, The Lord God says to Moses:

(Exo 19:9) And the LORD said unto Moses, Lo, come unto thee in a thick cloud, that the people may hear when I speak with thee, and believe thee forever. And Moses told the words of the people unto the.

Did you catch that? "That the people may hear when I speak with thee (Moses)."

Right there you have a revelation, in God's own Word, that He has spoken to people in an audible voice. When God talked with Moses, this entire gathering, of what many Bible scholars calculate was over six million people, literally heard God's voice!

So, you may be wondering, why doesn't God seem to communicate to us in this day and age?
Let's see what God says in His WORD. But first... let's read a bit further in Exodus.

Reading for the next several verses we hear God giving instructions about how they are to conduct themselves as an audience. They are not to touch the mountain. They may not approach God. There are definite boundaries. God is holy. Humans are sinful. This means God is not approachable by humans in their fallen state. Yes, God is love. But God is also just and will not tolerate sin. The only reason people today are able to draw near to God is because God has sent His Son to die for the sins of those who place their trust in Jesus Christ.That's why we pray "in Jesus' name".
Now let's listen to the next verse:

(Exo 19:16) And it came to pass on the third day in the morning, that there were thunders and lightnings, and a thick cloud upon the mount, and the voice of the trumpet exceeding loud; so that all the people that was in the camp trembled.

Can you see it? These descendants of Abraham, numbering in the millions, are standing still and looking up at this mountain. It's in the morning. The sun is still low in the sky. Suddenly, they hear this loud rumble. The animals get restless. The children perhaps hide next to their moms. The sky over the mount changes from a tranquil blue to a heart-pounding dark gray. It appears menacing. Lightening flashes and flickers over the mount. The enormous crowd stands transfixed much like today's Fourth of July crowds do at a firework's grand-finale.
A collective gasp goes up. Some babies begin crying. Just then, when your knees are knocking...this sound like a trumpet begins blaring from the summit of the mount.

At first is distant and faint. Then is keeps getting louder. Many people in the crowd begin to feel uneasy, because they recognize that no human can possibly carry the note this long. The blare continues to increase in decibels till it seems to cut right through you. How loud was this trumpet-like sound? "...all the people that was in the camp trembled."

We continue to read God's record of this event:
(Exo 19:18) And mount Sinai was altogether on a smoke, because, the LORD descended upon it in fire: and the smoke thereof ascended as the smoke of a furnace, and the whole mount quaked greatly.

Can you see this mountain smoking like a volcano? The only problem is- It's NOT a volcano!
The Lord is descending upon it from the upper atmosphere. The fire is coming from above the mountain and approaching the peak, until it touches down. This is NOT a UFO or an extraterestrial..This is the Creator of the entire universe touching Earth. The Israelites feel the earth begin to roll under their feet. I would imagine there was some vomiting going on. Perhaps some wet clothing? These people were seeing something no human had ever seen before, and have not seen since in history.

(Exo 19:19) And when the voice of the trumpet sounded long, and waxed louder and louder, Moses spoke, and God answered him by a voice.

First Moses spoke. Then God answered! These people actually heard something people have long wished they could hear since. The very VOICE of GOD!

In the following verses God reminds Moses to make sure no one crossed the boundaries in order to attempt to view God. Moses tells God that he has already told the people. God basically says 'I know- but tell them again!' Moses obeys.

(Exo 20:18) "And all the people saw the thundering, and the lightning, and the noise of the trumpet, and the mountain smoking: and when the people saw it, they removed, and stood afar off." Can you see the people backing up? They are terrified!

" And they said unto Moses, Speak thou with us, and we will hear: but let not God speak with us, lest we die.
(Exo 20:20) And Moses said unto the people, Fear not: for God is come to prove you, and that his fear may be before your faces, that ye sin not.
And the people stood afar off, and Moses drew near unto the thick darkness where, God was.
(Exo 20:22) And the LORD said unto Moses, Thus thou shalt say unto the children of Israel, Ye have seen that I have talked with you from heaven."

Exodus 20:19 describes the desire of anyone who has ever heard God's voice! They requested that from then on, Moses pass on to them what God wanted to say! This is the last time they will hear God's voice for 1,700 or so years! From that point on, God spoke to prophets, who then passed on to the people what God had said. The final prophet, spokesman for God, was to be Jesus Christ, the very one and only Son of God! Read Moses prophesy:

(Deu 34:10) And there arose not a prophet since in Israel like unto, whom the LORD knew face to face,
(Deu 34:11) In all the signs and the wonders, which the LORD sent him to do in the land of Egypt to Pharaoh, and to all his servants, and to all his land,
(Deu 34:12) And in all that mighty hand, and in all the great terror which Moses showed in the sight of all Israel.

(Act 3:22) For Moses truly said unto the fathers, A prophet shall the Lord your God raise up unto you of your brethren, like unto me; him shall ye hear in all things whatsoever, he shall say unto you.
(Act 3:23) And it shall come to pass, that every soul, which will not hear, that prophet, shall be destroyed from among the people.

You see, Jesus Christ is the voice of God to us. Jesus promised that His sheep would recognize His voice. Reject any voice that contradicts what God says in Scripture! That is 'the stranger's voice' that Christ warned us about!

In conclusion, I point out one last Scripture:

(Joh 12:28) Father, glorify thy name. Then came there a voice from heaven, saying, I have both glorified it, and will glorify it again.
(29) The people therefore, that stood by, and heard it, said that it thundered: others said, an angel spake to him.

(30) Jesus answered and said, this voice came not because of me, but for your sakes.

(31) Now is the judgment of this world: now shall the prince of this world be cast out.

(Joh 12:32) And I, if I were lifted up from the earth, will draw all men unto me."

I hope that you can now see from God's own Word that God's voice CAN be heard...but that we must always use God's written Word as the standard by which to judge any voice we hear. Test the spirits whether they truly are of God or not. Personally I do not think God normally speaks to us in an audible voice because we have His written Word. I do however believe that He reminds us of what He's said in His Word, and applies it to our own personal circumstances.He speaks to our hearts via His Word - like "a lamp unto our feet." God DOES speak to us, but I am afraid most of us, like those during Christ's earthly ministry, do not recognize IT!
Listen...take heed...and obey!