'Yes, I will.'
In short answers, as in tag questions, you have to use the same modal or auxiliary as the main sentence. It's like an echo, or a game of ping-pong. So, if the question is 'Will you..?', the response has to be either 'Yes, I will' or 'No, I won't'.'
If you're wondering where the 'I do' comes in, it's from the marriage ceremony. The celebrant asks the question 'Do you take ...to be your lawfully wedded wife/husband?', and the spouses-to-be echo this auxiliary by answering 'I do'.