Short answer. Possibly. Article 1640 gives a party evicted from the thing he received in barter a choice: recover what he gave, with damages, or claim damages only. But you can retake your car only while it is still in the other party's hands, and without prejudice to anyone who acquired it in good faith meanwhile.
What the law says
One who loses by eviction the thing received in barter may recover that which he gave in exchange with a right to damages, or he may only demand an indemnity for damages.
Civil Code, Article 1640 — Barter: Eviction. Read the full provision →
What the law says
he can only make use of the right to recover the thing which he has delivered while the same remains in the possession of the other party, and without prejudice to the rights acquired in good faith in the meantime by a third person
Civil Code, Article 1640 — Barter: Eviction. Read the full provision →
Eviction in a barter gives you a choice
What happened to you is an eviction: a person with a superior right took the motorcycle you had received in the trade. Because barter is a two-way exchange, the Code lets the evicted party undo his side or be compensated. Article 1640 says: One who loses by eviction the thing received in barter may recover that which he gave in exchange with a right to damages, or he may only demand an indemnity for damages. So you may either ask for your car back together with damages, or leave the trade standing and simply claim damages for your loss.
Which option to take
The election is yours, and it turns on what you actually want. Recovering the car unwinds the exchange and puts you back roughly where you started, with damages on top for the harm the eviction caused. Demanding indemnity only leaves the barter in place but requires the other party to pay you for what you lost when the motorcycle was taken. If the car still exists and you would rather have it than money, the first route appeals; if the car is gone or you would prefer compensation, the second does the job.
The limits on getting the car back
The right to actually retake the car is hedged by two conditions. The article provides that he can only make use of the right to recover the thing which he has delivered while the same remains in the possession of the other party, and without prejudice to the rights acquired in good faith in the meantime by a third person. So the car must still be with the person you traded with, and anyone who has since acquired rights in it in good faith is protected. If your trading partner already sold the car to an innocent buyer, you cannot pull it back from that buyer — you fall to the damages remedy.
Act quickly and prove the eviction
Time is against the recovery option, so move while the car is still in the other party's hands. Be ready to establish that the loss of the motorcycle was a genuine eviction — a person with a better title enforcing that right — rather than a mere breakdown, theft, or private repossession, because the remedy depends on it. If the car has already passed to a good-faith third person, focus on your claim for damages against the party you traded with. Keep the barter documents, proof of the superior title, and a record of the car's whereabouts to support whichever remedy you pursue.