If you take God as the ground of all being - the driving force behind all that is possible and the component that makes all things what they are - then I do not believe you can limit God by what is "possible." You can argue that God adheres to His own rule and does not violate His laws of nature (excepting, say, miracles), but you cannot say that it is impossible for God to make a square-circle, or heavy rock He cannot lift, because the human idea of what is possible is not the dominant one. To think otherwise is to assume there is a force higher than God that is limiting Him, and once you do that you've created an endless loop with no dominant force or being at the end of the tunnel.
Within Euclidean (or even non-Euclidean) geometry it is impossible for even God to make a figure satisfy the conditions of being a square and a circle at the same time. One of the properties of a circle is that at any point along a circle, you can construct one and only one tangent line. At the vertex of of any polygon, unless the angle of intersection of the sides is 180° there is no tangent line. While it is true that God need not use our conception of geometry, he can't within the selected axioms of geometry make a square that is a circle. (Altho in non-Euclidean geometry, anyone can make a quadrilateral that is a circle since in non-Euclidean geometry a quadrilateral is not constrained to having the sum of its angles be 360°.)
As for the old bromide about whether God can make a rock too heavy for him to lift, the less said about it the better.