You can try, but it seldom works. Correctional staff are not permitted to relay personal messages to inmates as a matter of facility policy. The rules exist for good reason: if staff started passing along phone messages from family members, the volume of requests would be unmanageable and the system would break down quickly. It is not that individual staff members do not want to help. It is that the rules prohibit it.
The most reliable way to get a message to your inmate is through a letter. Send a short note letting them know you want them to call, include your phone number clearly, and it will reach them within a few days through normal mail. InmateAid's letter service lets you send that kind of quick note from your phone without printing or stamps if you need a faster or more convenient option.
If someone else who is already on the approved phone list has recent contact with them, they can also pass the message along during a call.