Translation:I will pay today.
As Japanese is a very contextual language as such it is fine if not more natural for the お金 to be implied. Additionally, in most cases it would be better to leave out 私 as when used excessively can make you seem self centered. Pronouns like 私 and あなた are generally left out unless it is not obvious who you are talking about. In the example of this sentence you would only need 私 if you are trying to stress that it is you rather than somone else who is paying.