In addition to what the previous poster said, that can also be "Whom do I have the pleasure of speaking with?" Phrasing English sentences with the preposition at the beginning (like in Spanish) instead of the end is generally much more formal. In some cases, like this, it sounds natural and appropriate, but in others, it sounds extremely unusual (e.g. you will almost never hear an English speaker say "For whom is this?") Generally, unless you're trying to sound more formal, you should put prepositions that are at the start of Spanish sentences at the end of English sentences. (Not that I'm advising against "With whom do I have the pleasure of speaking?" specifically. I'm making a note for general usage.)
As for "whom" - by strict prescriptivist standards, "whom" is used instead of "who" when you're referring to an object instead of a subject (e.g. a situation where you'd use "te" instead of "tú" in Spanish). However, it's almost completely absent from regular speech, and it often sounds weird to use it even where it's grammatically appropriate (e.g. "Whom are you going with?" would sound odd to most people, even though it's called for by strict English standards.) Unless you're trying to please your English teacher or are trying to come off as proper, you shouldn't bother with "whom" (and because Spanish just uses "quién" in those cases anyway, it's much easier on you to just translate it to "who".)
That said, I'd recommend the previous poster's first phrase if you're trying to be formal, and their second phrase if you're not trying to be formal.