Not in the sense that he can move an immovable object or resist an irresistable force.
God is not the kind of guy you can sneak shit like that up on. It's find and well to sit around hypothesizing with words - "God must be able to make a creature with free will and without free will, or else he'd not be omnipotent" "God can break logic" "God can do whatever he wants, including evil, so he's not good, then, is he?"
The problem with hypothetical statements like that is in the use of words. Jabberwocky mentioned a wonderful thing that C.S. Lewis said in The Problem of Pain:
His omnipotence means power to do all that is intrinsically possible, not to do the intrinsically impossible. You may attribute miracles to him, but not nonsense. There is no limit to His power. If you choose to say, "God can give a creature free-will and at the same time withold free-will from it," you have not succeeded in saying anything about God: meaningless combinations of words do not suddenly acquire meaning simply because we prefix to them the two other words 'God can'. It remains true that all things are possible with God: the intrinsic impossibilites are not things but nonentities. It is no more possible for God than for the weakest of His creatures to carry out both of two mutually exclusive alternatives; not because His power meets an obstacle, but because nonsense remains nonsense even when we talk it about God.
Summary: Claiming that God is not omnipotent because He cannot move an immovable object is the same as saying God isn't omnipotent because He can't put your car in both reverse and first at the same time.
God is not omnipotent if being omnipotent means he can do nonsense. God is only capable of doing the possible.
Even the insanely complex, only theoretically possible.