The clan lived in the frozen lands of Arctika where they would viciously attack and kill any intruders that passed their territory. They were a rival clan of the Lin Kuei; however, they were the weaker of the two and thus feared the frost ninjas. Taven passed through Tengu-held territory and defeated their leader, who submitted and allowed the ancient Edenian to pass. Certain members of this clan did, on occasion, go rogue and become frost ninjas, who were a threat to anyone who passed the icy lands alone.
No members of the Tengu are mentioned, but the only known member of the clan is Wu Lae, who's their leader, he's a strong ninja and wears a black garment, wielding a scythe, he was ultimately defeated by Taven.
In Armageddon's Konquest mode, after defeating Wu Lae you have the option to perform a fatality on him. Doing so would unlock Kitana's Alternate Costume.
While the Lin Kuei are notorious for wearing blue ninja garments, the Tengu are recognizable by their orange-colored apparel.