Should you recuse yourself from the hiring committee if you have had a past romantic relationship with an applicant?
I will almost guarantee that your university has a Compliance office. Here's the one for my university; you'll notice that it has both a number of links to written guidelines, as well as phone numbers for an Ethics hotline. Your university may not have the exact same thing, but there are people there whose job is to answer these types of questions. Make use of them.

That said, from my completely uninformed standpoint, your situation sounds like a conflict of interest. If I was in a similar situation I would definitely recuse myself.