Yes, however as there are HUGE mining farms with millions of times the processing power of any normal computer, the odds of you ever finding a block are extremely small.
What you can do, is join a mining pool, which is very easy to do. A pool is essentially a group of miners who combine their processing power to process blocks. Everytime a block is mined, the BTC is distributed to all the miners proportionally to how much processing power they contributed. You wont get alot doing this unless you have a high end graphics card, and even then you may not even make a profit unless you get free hydro.
At this point, its much more cost effective to just buy BTC with your money rather than invest in a mining rig.