Hi Everett,
If conversation is going really well with someone else on a dating site, phone numbers are often exchanged as soon as within a week or two. But, in the end, what matters more is what you feel comfortable doing.
If you don’t feel comfortable giving him your phone number, either tell him that you would like to keep communicating through the dating site for a little while longer, or give him another option by which the both of you can communicate. For some people, that option is through personal emails or even social media.
At the end of the day, how comfortable you feel is most important. If he truly likes you, he will respect whatever decision you make.