current category ID into a variable

It already is: $cat is a global variable in WordPress that holds the category ID for a category query.

I’m no php expert but:

You can access the current category from the global variable $cat . I’ve used it before but for example <?php $my_variable = $cat; ?> I cant seem to get to it right now but https://codex.www.remarpro.com will have information on it if you just search for $cat .