Yes, as long as it doesn't involve moving the pinned piece.
A Question on Rules
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Picture it as the game ends when the first king is taken. Moving your own king into check - even if the checking piece is pinned against your opponents king would still result in your own king being taken first.
Yup.
A king can never move to a square threatened by an enemy piece, even if that piece is pinned.
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When a piece is pinned to the king (and therefore cannot move) can it be used to prevent the opposing king from moving into a space that would otherwise be threatened by that piece?