The paradox boils down to question its self.
Specifically the term: "...a rock so heavy god could not lift it."
Such a thing is logically impossible.
But lets return to god first:
God is omnipotent, which means that he is able to do *anything*. Well the set of *anything* only contains all real things/events. It cannot contain non things/events.
Its the same as the concept normal numbers vs imaginary numbers. No matter what i do i cannot give you the square root of -9 oranges (or 3i oranges). If i had X oranges no matter how many i added, took away, arranged, or changed my oranges i would never end up with 3i oranges to give you. This is because 3i oranges is not a 'thing' to give. If i had a million times more influence over the universe, i would still not be able able to achieve this goal. If i had a million billion billion times more influence it would still not be possible.
Even if i had infinite influence over the universe, i still cannot achieve the goal. This is because goal is not a goal at all. It is not a 'thing to achieve' because it is not a thing at all. Its a non-goal.
For a goal to exists it must be a real goal, not a non-goal. The place i want to get to must indeed be a place to get to.
Now the 'rock god cannot move' is not a real thing. Because god, by definition, can move anything that exists, a 'rock god cannot move' is like saying a 'motionless rock traveling at 100km/h.' It is oxymoronic term, and violates the very definition of what it is.
Other examples are:
A triangle with 4 corners
Red paint that is blue
These are not real things. They are non-things, and do not fall with in the set of 'everything'
So the answer to the question is NO. God cannot create (or move) a rock so heavy god cannot move it. But this does not violate god's property of 'being able to do/create everything (omnipotence)' because a 'rock so heavy god can't lift it' is not in the set of 'everything.'