I used to be able to do it. But no more. So it must have gone away in a fairly recent software "upgrade."
I can understand why it may have been removed as an option. Some members would delete their post(s) days or weeks later and it can really disrupt the continuity of a thread. The feature was handy when initially posting a response, for example when two people post the same answer at nearly the same time, or if a "quote" mistake was made. Perhaps a compromise could be a 'delete post' option that can only be used within a specified amount of time of the initial posting (e.g. 5 minutes).