This is known as a pseudo-question. It’s like asking, “Can God win an arm wrestling match against Himself?” or, “If God beat Himself up, who would win?” or, “Can God’s power defeat His own power?”
The question is nonsense because it treats God as if He were two instead of one. The phrase “stronger than” can only be used when two subjects are in view, for example, Bill is stronger than Bob, my left arm is stronger than my right arm, etc. Since God is only one, and since He has no parts, it makes no sense to ask if He is stronger than Himself. That’s why this is a pseudo-question. It proves nothing about any deficiency in God because the question itself is incoherent.
This pits one aspect of God’s ability against another—in this case, His creative ability against His ability to lift. The goal is to show that there are some things God can’t do, thus undermining the Christian concept of an omnipotent Creator. This illustration, however, miscasts the biblical notion of omnipotence, and is therefore guilty of the straw man fallacy.
Omnipotence doesn’t mean that God can do anything. The concept of omnipotence has to do with power, not ability per se. In fact, there are many things God can’t do. He can’t make square circles. He can’t create a morally free creature who couldn’t choose evil. He can’t instantly create a sixty-year-old man (not one that looks sixty, but one that is sixty). None of these, though, have to do with power. Instead, they are logically contradictory, and therefore contrary to God’s rational nature. The “Can God make a rock so big He can’t lift it?” challenge is no threat to Christian theism.