It is speculated that Trowa's place of origin was either Earth or L3 Colony cluster. He ultimately ended up on L3 Colony, if one goes in accordance to Episode Zero. In the anime, during "Episode Twelve: Bewildered Soldiers" Trowa automatically considers the L3 Colony his origin it seems. He called it "my colony". In any case, whether he was born there or not, he considers it to be where he is from.
By rumor over the Internet it seems to be widely accepted that his ethnicity is Latin or Latin American. From what most profiles other than those show, however, his heritage is unknown. From mere belief I assumed it is just the attempts of others. Latin (American) could have been chosen because of the heritages of the other characters.
According to GundamOfficial.com Heero Yuy is Japanese. Duo Maxwell is American. Quatre Winner is Arabic. Chang Wu Fei is Chinese. Zechs Merquise is Northern European. Lucrezia Noin is Mediterranean. Treize Khushrenada is Aryan. Lady Une is German.
Therefore he just "couldn't" be any of those.
Some places say the producer of the show said he was of Latin origin in regards to heritage. Therefore, the American part is highly questionable. It is one or the other. Latin American is not the exact same as Latin.
Some have looked to the origin of the name Trowa, which is supposedly the Romanization of the French word "trois". Italians, Spaniards, Portuguese, French and Romanians are popularly called "Latins" by other Europeans because of their distinctive Roman roots. Therefore, while it is a possibility he could be of French ethnicity, the name he goes by lacks in significance since it isn't really his name.
What gives some significance, though is how in the television series, the five Gundam Pilots land at separate areas. The Gundam Wing Series Novelization expands on this, telling where the pilots landed in book one, "Operation 1: Departure".
Heero ends up being around the JAP point in the Asian Area, or pretty much Japan.
Duo is near the island of Guam, a United States island territory.
Trowa lands near the Iberian Peninsula.
Quatre lands around the Arabian Peninsula.
Wu Fei lands near the Yangtze River in East China.
Now, if one looks back to what Gundam Official gave as the Gundam Pilots' ethnicities, all of them seem to land in areas that are associated to their lineage. If one were to follow that trend, a person could assume Trowa is Iberian, which is the in the extreme southwest of Europe. It includes five countries/territories: Spain, Portugal, France, Andorra and Gibraltar.
In note to this, some places have noted the L3 Colony cluster is mainly comprised of those of the nationality with Slavic descent. Slavic is pretty much Indo-European.
Aryan, Treize's origin, is a 19th-century term for Indo-European speakers. Some people have come to believe he is Trowa's older brother.
In other cases there has been claim that Catherine is of Russian decent, but the source this information came from is unknown. This also "supports" the belief that he could be Russian if he is indeed related to her as implied in the manga Episode Zero.
While there is still nothing concrete, from what is given, it seems that there is some possible hinting that Trowa is European if anything.