It is possible, but the past tense is more likely. The present perfect is a present tense and so is about the current state. That would normally be used with a present tense modal phrase
Jo has stolen the necklace
This tells us about Jo now; she "has" the "experience of stealing" in her past.
I might be Jo who has stolen the necklace.
There is no real need for the present perfect here, and most people would use the past tense in this particular situation. But models don't have past tense.
The perfect structure is also used with models to talk about the past. That would go naturally with a past tense.
It might have been Jo who stole the necklace.
Here we are speculating about the past.