Easy, just pipe it to wc:
grep -Ro "searchTerm" . | wc -w
-R means recursive, -o means it will return only the matching words. Then you pipe it into wc (wordcount) -w means it will count words. Might be a bit trickier if the pattern you are searching for includes spaces, in which case they have to be escaped.
Note that the -w option will return the number of matches, so you have N matches on 1 line, it will return N, not 1.