This paper introduces a method to construct Hermitian representations of Lie algebroids by a geometric quantization procedure. Lie groupoids play an important role in the study of manifolds with boundaries or corners and in Poisson geometry. In this work, the author generalizes the construction of representations to the case of Lie algebroids and Lie groupoids. He first recalls the relevant notions, namely the notion of a Lie groupoid or a Lie algebroid action on a map. Then he constructs a prequantization line bundle. The main theorem follows. Finally, it is showed how the well-known orbit method, developped by Kirillov, and the nice results for reductive Lie groups can be extended for Lie groupoids.