As we near the end of tractate Nazir, the discussion turns to
slaves. Can a slave make a nazarite vow? Yes, and not only
that but, according to the mishna, the nazarite vow of a slave
is more stringent than one of a woman, because a man can annul
his wife's vow but cannot annul his slave's vow. If a slave's
master disapproves of the slave's vow, it appears that the
master's only recourse is to free the slave. (62b)
(I assume, though I couldn't confirm one way or the other in the
Aramaic text, that this is talking about an eved ivri, a Jewish
slave. Jewish slaves get freed eventually anyway, so this would
just mean accelerating the schedule, and I would be surprised
if non-Jews can (per torah) take nazarite vows. (Of course they
can vow anything they like, but it wouldn't be governed by torah,
I would think.)