You can try calling, but do not count on it working. In most facilities, the rules prohibit staff from modifying an inmate's approved phone list based on a request from an outside caller. The phone list exists as a security measure and changes to it are supposed to go through the inmate, not through family or friends calling in. That said, some staff members will make an exception for a simple request like adding a phone number, particularly if you are polite and the ask is small. It varies entirely by facility and by who answers the phone.
The reliable method is a letter. Write a short note to your friend with your phone number clearly written at the top and send it through InmateAid or standard mail. Once he has your number, he can add it to his approved call list through his housing unit officer or counselor. That process is handled on his end from inside the facility.
A postcard works just as well for this purpose and may feel more informal if you want to keep it brief. Either way, getting the number to him in writing is the approach that actually works consistently.