Can a pinned piece give check in xiangqi?
These answers restate the rules implemented by our open-source engine, which follows the WXF laws for movement, checkmate and both repetition rulings: a side that forces a repetition by perpetual check or perpetual chase loses rather than drawing. The chase half has not been validated against the official casebook. Where an answer refers to a specific position, that position lives on the linked reference page, where the build verifies it before publishing.
Direct answer
Only with a move that stays on the pin line. If a piece is pinned, meaning moving it off its line would expose your own general to capture, that move is illegal outright, regardless of what it would achieve, including giving check to the enemy general. A pinned chariot, cannon or soldier may still move along the line, and such a move may give check. Legality is checked against your own general's safety first.
The strongest example: the flying general pin
A single piece standing alone between the two generals may not leave the file: not to capture, not to block something else, not to give check, because each such move would leave the two generals facing on an open file. A horse, elephant or advisor always leaves the file when it moves, so it is completely frozen; a chariot, cannon or soldier may still move along the file. See the flying general rule for how that pin arises.
Ordinary pins work the same way
A piece shielding your general from an enemy chariot or cannon along a rank or file is pinned in the everyday sense, and the same test applies: any move that would open that line is illegal, whatever else the move might have done. There is no exception for a move that happens to be a strong attacking idea.
Related questions
Does this mean pinned pieces are useless?
Not at all, they still attack and defend the points they cover and block enemy lines; they simply cannot move off the line.
Can a pin ever be broken by giving check elsewhere?
No. Legality of the pinned piece's own move is unaffected by threats you create with other pieces.