Learn English – Ends of verbs after words “which”, “that” & “who”

The girl who love(s) kittens.

The construction is called a relative clause, and "who" here is a relative pronoun.

If the clause is in the present tense, and has a third-person singular subject, then yes, the verb should have the suffix (e)s.

Wikipedia says the clause also should be in the Indicative Mood.

Note that this only works for third-person subjects:

You, who love kittens, come here and see a new kitten clip I've just found on YouTube! (a bit high-hat, but anyway: the second-person you licenses the use of love, not loves)
We, who love kittens, gather in this quiet park every Saturday. (first-person subject we --> love, not loves)

An example from a poem: the poet addresses the Moon (second-person: you) and thus uses rise, not rises in the relative clause starting with the relative pronoun "that":

Enormous moon, that rise behind these hills
Heavy and yellow in a sky unstarred
And pale, your girth by purple fillets barred
Of drifting cloud, that as the cool sky fills
With planets and the brighter stars, distills
To thinnest vapor and floats valley-ward,—
You flood with radiance all this cluttered yard,
The sagging fence, the chipping window sills.

The author of one poetic blog explains this in this way:

Interesting that she uses "rise" for the moon in line 1 and not "rises." I think she is addressing the moon—"you that rise."

At the same time, she uses "sky fills" and "cloud ... distills". (these are third-person subjects)

Reference:

• English Verbs: third person singular present - Wikipedia
• Some interesing bits on the history of verbal suffixes - ELU