I know this is an old and kind of silly paradox, but really think about it. It's a good question. If your god truly were all-powerful, could he create a rock he cannot lift? If not, he is not all powerful, and if he cannot lift it he is also not all-powerful.
That seems like a good argument but I will analyse it in this post to make sure that the statement is not an accidental play on words. First I want to generalize the statement.
Can God make a rock he can't lift?
Notice that assuming that God is all powerful, there is no such rock, it doesn't and cannot exist. It is like saying that 2 + 2 = 5. So I will now rephrase the question.
Can God make something that is impossible?
Making something which is impossible is itself impossible and a logical contradiction. The question can further be rephrased.
Can an omnipotent God do something impossible?
This whole statement is a contradiction because an omnipotent being can do anything and so should even be able to do the impossible. Yet the impossible is something that cannot ever be done even by an omnipotent being. So we either have to say that an omnipotent being doesn't exist or nothing is impossible.
However, the rock analogy is a perfect example of the impossible and there are many more. Can you make something a dog and not a dog at the same time? Can you make a perfect world that has evil? There and many more things are impossible and we are forced to the conclusion that some things can never be done.
The conclusion to this is that an omnipotent being, a being who can do anything cannot exist. The best a being can do is be able to do anything which can be done. However, that is not omnipotence.