Can I rejoin a military branch after I get chaptered?

Lots of good answers here, I side with my fellow NCO. They at putting you out because health reasons are keeping you from performing in your MOS, and you are in a small MOS pool. So far they may or may not have offered a reclass to a different MOS,, or there is not an MOS to fight your health problem. You are going to have to wait to you get your Re-entry code to really ask questions, when you get that you can check with your retention/enlistment NCO. Regardless you will have a fight on your hands, the chapter will stay with you and will require a enlistment waiver which will take some time. .

PFC (Join to see) "Getting chaptered due to medical reasons."
If Im reading that right, your still in and in the processing of separation?
If so, your question can not be truly answered yet, need to see what you receive as an RE code.
However, the Army does not tend to medically separate those that can recover from injury or illness sufficiently to be eligible for military service... thats the whole point of being medically separated, it was decided you can not serve as is, or after treatment and recovery....

Thats not a solid line in the sand,,,, reclass could have been offered and turned down, but as your already in a low density "soft" MOS I doubt thats the case.

Or Mil medical treatment is not sufficient to heal you, but civilian procedures are...again not likely but possible.

Then there is length of recovery...if it is anticipated to be a long time ....years, or longer, separation is likely the result.

No one will know better than your local recruiter, who will have the resources on hand or a phone call away to find out