Usually trip action requires one to use an unarmed attack or a special trip weapon. Is it possible to trip using a natural weapon?
It can trip, but not with a natural weapon.
The D&D 3.5 Player's Handbook, p.158, is clear that (unless you have a tripping weapon or specific ability stating otherwise), tripping requires an unarmed attack:
You can try to trip an opponent as an unarmed melee attack [...]
Making a Trip Attack: Make an unarmed melee touch attack against your target. This provokes an attack of opportunity from your target as normal for unarmed attacks.
Rules Compendium, p.16, clarifies that while a monster can make unarmed attacks, it cannot make one with a natural weapon:
A creature that has a natural weapon, such as a claw or slam, is considered armed. It can make unarmed attacks, but it cannot use its natural weapons as if they were unarmed attacks, nor can it apply abilities that affect only unarmed attacks to its natural weapons.
Note that this contradicts the D&D 3.5 FAQ, which has a habit of putting forward the Sage's opinions on what would be reasonable, rather than what the rules strictly say. I'll share it here anyway, since it makes for a reasonable house rule. On page 98:
A creature can make a trip attack with just about any natural weapon, although the DM must exercise some common sense in the matter. Claw and bite attacks are excellent for trip attempts, as are tentacle attacks. Since tripping in the D&D game involves grabbing a foe and pulling him down, stings, gores, hooves, and most slam attacks should not work for tripping (although tail slaps work).
[...] In either case, a monster making a sunder or trip attack follows all the rules a player character uses for the attack in question, including provoking an attack of opportunity.
The trip rules specify “unarmed attack” rather than “unarmed strike” specifically. The rules don’t explicitly call out the distinction between the two, which makes me dubious that there is a distinction (and that all of the authors were aware of it and used the terms consistently). But the rules do talk about fighting unarmed and mention natural attacks as well as unarmed strikes, so it is plausible that unarmed strikes are but one form of unarmed attack, and natural attacks are another form of it.
If you buy that, then yes, natural weapons can be used to trip.
Otherwise, absurdly, the rules seem to leave them out. Note that numerous creatures make trip attacks with their natural weapons—iconically, wolf bites get a free trip after—but you could just see those as exceptions to the rule.
But since it is absurd that natural weapons would not be able trip, I’m incline to believe that unarmed attack vs. unarmed strike argument here, where otherwise I’m not too sure about it.