Teachta means " Messenger; envoy, representative", so I don't see how it's all that misleading to non-Irish natives, though it would be clearer if the answer was "I'm a Dáil Deputy", as I'm sure that there are one or two Irish natives who associate the word "deputy" with "sheriff" too.
And I disagree with the suggestion that "to native Irish the translation is member of parliament". It is extremely rare for anyone in Ireland to refer to a TD as a "member of parliament", even though that term is in widespread use in Ireland, due to coverage of UK politics. The terms just aren't interchangeable. The Irish for "Member of Parliament" is Teachta Parlaiminte or Feisire, and we don't even use teachta for "Member of the European Parliament", which is Feisire de Pharlaimint na hEorpa.