Yes Faith is a work, its the act/deed of the man or women who has been #1 Made Righteous by the sole obedience of Jesus Christ Rom 5:19 and #2 who has been born again by the Spirit of God, for Faith is the fruit/work of the Spirit Gal 5:22
22 But the fruit of the Spirit is love, joy, peace, longsuffering, gentleness, goodness, faith,
The word fruit karpos means:
(a) fruit, generally vegetable, sometimes animal, (b) met: fruit, deed, action, result, (c) profit, gain.
In fact the word also signifies:
Metaphorically, that which originates or comes
from something; an effect, result;
a. equivalent to ἔργον, work, act, deed: