That's actually a really good question, and I'm not entirely sure myself.
RAW, my first instinct is to say you can't, because a grapple is a
check, not an attack. It doesn't auto fail or succeed on a natural 20, for instance. Weapon Finesse lets you use dex on attacks, so the case should be closed. But there's one particular RAW loophole. Observe the text of Weapon Focus (and Specialization, if you scroll down, too):
Feats :: d20srd.org
"Choose one type of weapon.
You can also choose unarmed strike or grapple (or ray, if you are a spellcaster) as your weapon for purposes of this feat."
Now, I like to rule logically. Something's either a weapon, or it isn't. If you can treat something as a weapon for one generic combat feat, why not others? And if it's a weapon, you're attacking with it. Weapon Focus, in fact, modifies
attack rolls.
So...if you'd allow someone to take Weapon Focus (grapple), then Weapon Finesse should work. If you wouldn't, probably not. Very murky, though. Personally (IMO, etc...), I think of grappling strictly as a check, not an attack. But at the same time, I like the idea of a dex grappler, and love that Tome of Battle made dex-based tripping possible. I'd really like to allow it...