Well, in use - any of these can be used but the traditional use is "piqued."
To "pique" one's attention is to stimulate (Oxford Languages). Originally from the French, it was a word meaning to "prick." In the original English use it most often had a negative connotation or resentment. However, in more common or modern usage it means to arouse curiosity or interest in a subject.
To "peak" - when used as a transitive verb, can mean "to cause to come to a peak, point, or maximum." This can have appropriate use for "peaking one's attention." (Webster's).
Likewise, to "perk" is to bring something to the top - so again, it could be used to "perk" one's attention.
All that said, what is traditionally meant is to "pique" one's attention. English can be funny at times, especially since even improperly used words can become "accepted" if usage is high enough.