There is no verb "to speak" here. Is it a mistake? Or is it implied by the question?
In Irish, if you have the ability to do something, you "have" it. So Tá Gaeilge agam (lit. I have Irish) means "I speak Irish" as in "I have the ability to speak Irish."
You'll even hear people in Ireland say "I have Irish (or French, Spanish, etc.)" in English.