Your sentence is grammatically sound, but isn't idiomatic and doesn't convey the meaning you intend.
Since a queen is the most powerful piece in chess, the typical case is to promote your pawn to a queen, or to queen your pawn. Much less often, it can be advantageous to promote the pawn to a piece other than a queen.
Exchange (a pawn) for a more powerful piece of the same colour,
typically a queen, when it reaches the opponent's end of the board
The promotion of a pawn to bishop, knight, or rook in chess m-w
This happens more frequently in chess problems which feature underpromotion as a theme. (Since it's uncommon in actual games, it's often overlooked in a problem.)
The verb here is to underpromote (a pawn) (to a rook, bishop, or knight). However, you would usually say "It's better to promote to a rook in this case", rather than underpromote. The verb underpromote would be used in cases like the webpage below: "When is it better to underpromote," where it refers to underpromotion in general.
Although the verb to underpromote is used in the chess world, I don't see it in the few dictionaries I've checked. I've need heard or seen rook, bishop, or knight used as a verb for pawn promotion and they sound quite odd, perhaps also because to rook and to knight have other meanings outside of chess.
To rook is "to defraud by cheating or swindling" m-w. I could understand White has rooked his pawn to prevent stalemate to mean that White cheated by surreptitiously removing a pawn from the board to prevent a stalemate.
Don't get rooked by scams
Unfortunately, con artists target senior citizens. S. Polgar and
Douglas Goldstein; Rich as a King: How the Wisdom of Chess Can Make
You a King
Another difficulty: prices. In recent years, Paris has earned the
reputation of being Europe's most expensive city. Ergo, everybody is
convinced that you get rooked in France no matter where you go.
But that just isn't so. Skiing, Oct. 1967, p.127
Some reasons why you would want to underpromote:
A knight gives check, checkmate, or forks more than one piece upon promotion where a queen would
Promoting to a queen would
stalemate your opponent (giving them no moves and thereby tying a game you could otherwise win).
Other, more technical cases are discussed in the links below.
"A Guide to Underpromotion in Chess"
"When is it Better to Underpromote?"
"Promotion (chess)" at Wiki has underpromotion statistics