Can you castle when the piece that is preventing you from castling is pinned?
Answer is no. I'm assuming you're talking about the situation where the "check" piece is pinned, and King tries to castle through piece's check. This requires 2 explanations, so here are both:
-King cannot move into/through a check by a pinned piece, because that piece will take your King before you can take the other King. It's about which King is captured first.
-King castling is treated is making two moves in a row, one of which moves into a check by the pinned piece.
Can you castle when the piece that is preventing you from castling is pinned?
No.