No, so far as I know, there is no way to search by the person who deleted a question. As of 2015, though, there is a way to limited way to get a list of deleted questions using SEDE. This meta answer explains in more detail:
In short, if you got to https://data.stackexchange.com/politics, you can compose a SQL query to search in the
PostsWithDeleted table. This will provide only a limited selection of data: the postid (letting you find the question), creation date, deletion date, score, id of parent question (if an answer) and tags (if a question).
That's not much to go on, but it's not supposed to be easy to find deleted questions. The other answers in that meta question discuss other options, but none that are likely to do what you want.