The promise of the Holy Spirit's coming is attributed to Jesus Christ in the New Testament. He mentioned this in several passages, notably in the Gospel of John. However, if you're considering the figures listed in your question, the closest answer would be "The Father," as Jesus spoke about the Father sending the Holy Spirit (for instance, in John 14:16-17).
Joel, on the other hand, prophetically spoke about the outpouring of the Spirit in the Old Testament (Joel 2:28-29). John the Baptist also mentioned the coming of the Holy Spirit in relation to Jesus but did not promise it in the same manner.
Therefore, while Jesus is the one who directly promised the Holy Spirit, if the context allows for the divine promise made about the Holy Spirit, "The Father" could be considered the most appropriate answer among the provided options.