Is a turtle a reptile?

Turtles are reptiles.
Turtles (including tortoises and terrapins) belong to the order Testudines, which is a part of the class Reptilia. 
The characteristics that turtles share with all other reptiles include:
Scales. Reptiles do not have feathers, fur, or slime, which respectively characterize birds, mammals, and amphibians.
Large-yolked eggs. Unlike amphibian eggs, reptile eggs retain water and do not need to be submerged. Reptile eggs are typically leathery, unlike bird eggshells, which are typically made of brittle mineral. Also, a few reptiles are viviparous, meaning they bear live young—however, they do so by retaining their eggs inside their bodies, rather than the more complex means by which mammals incubate fetuses.
Ectothermia, or cold-bloodedness. Reptiles cannot regulate their own body temperature and rely on the external environment to keep themselves able to move and the chemicals in their cells able to react. Turtles may bask in the sun to warm themselves, and they may hibernate during colder months when activity is impossible.