Unfortunately no. Inmates initiate all outgoing calls and there is no way to call them directly. That is standard policy at every correctional facility in the country regardless of the circumstances, including a phone number change on your end.
This means the burden of getting your new number to him falls entirely on you through other channels before he can reach you. If he dials your old number and gets a disconnected message or no answer, he has no way of knowing what happened or how to reach you without someone getting the new number to him first.
The fastest options are a letter or postcard sent through InmateAid with the new number written clearly in the body of the message. Allow about a week for it to clear the mailroom and reach him. If timing is tight and you know someone else on his approved call list whose number has not changed, they can relay the new number verbally the next time he calls them.
InmateAid also provides notification coupon codes at no charge specifically for situations like this. Email aid@inmateaid.com and ask for one. That gets a letter out to him quickly with the new number so the gap in communication is as short as possible.
Once he has the number and it is added to his approved call list at the facility, he can reach you again. Get that letter moving as soon as possible so he is not left wondering why you are not picking up.