We say “Can I beg a pardon of you?“
And I wonder if “Can I beg you a pardon“ is grammatical.
Perhaps wotcha means 'Can I ask a favour of you?' - even then, though acceptable, it sounds pretty mannered. It'd be more natural to ask 'Will you do me a favour?' or - to be extra polite 'Would it be all right if I asked you to do me a favour? [Just say No if you'd rather not; I know I shouldn't really ask.]'
If you use 'pardon' it's either the polite/conventional apology for doing something socially wrong, or just a request for repetition: '[Beg] pardon - I didn't quite catch that'. (That's apart from the case where someone does beg for a pardon, because, for example, they don't want their head chopped off!)