In the capture window you can use standard Org commands. So at any point you could hit
C-c C-q (the default binding for
org-set-tags-command) to add tags.
Refer to the Setting Tags section in the Org manual for more details about tag completion.
As noted in the comments, this doesn't quite work. By default tag completion is derived from the current buffer, and the capture buffer is narrowed so that there are no tags to choose from. (You could widen the buffer, but that's clunky.)
You can use
org-capture-hook to set the available tags for the capture buffer.
For example you can use Org's global set of tags with this:
(setq-local org-tag-alist (org-global-tags-completion-table))))
This will let you picks tags from any of your org agenda files. If you only want to see tags for the capture file, try this instead:
(setq-local org-tag-alist (org-get-buffer-tags)))))