Is it possible to convert a JAMMA controller to a console?

I tried to look this up myself, but I could hardly tell if it’s possible. Is it possible to convert a JAMMA controller to a console?

yea, the easiest way is to just hack a controller and solder the wires from the jamma controller to the contacts on the hacked controller for whatever console you want to use.

If you want it for multiple consoles you’d probably have to do the project box solution.

Is there any way I can buy a converter?

Probably, but your description is way too vague to have any clue what you have in mind. If you’re looking for a converter of some kind, maybe you should link up or post of pictures of what it should go into, and what goes into it.
Something like:
I want to plug this:
<insert picture>
into this:
<insert picture of other thing>