This question has a fundamental assumption that is not stated in the question: God can do anything that is Possible. This statement must logically be intrinsically true because: Even God can't do something that is not possible to be done. The "Stone Question" is logically impossible to ask, as it logically translates to: Can God do something that is not possible?
The answer must be No, as by definition something that "can not be done" can not be done. This is equivalent to saying something like "Can God make Zero equal One?" Logically and mathematically, this is impossible, as by definition zero and one (and all discrete numbers) by definition can not have the same value as another discrete number.
Therefore, the answer to the question is: (Drum Roll, please) No. God can not make a stone so heavy that He can not lift it. Because if God is all-powerful (meaning that he can do anything that is possible to be done) it is impossible for Him to create a stone that He could not lift, because it is not possible to do so.