This paper proposes a new optical angle sensor, in which a mode-locked laser is employed as the light source, and chromatic dispersion of a collimator objective is utilized to detect the angular displacement of a target of interest. In the proposed method, each of the optical modes in the femtosecond laser beam reflected from the reflector mounted on a target of interest is separated from the others by chromatic dispersion of a collimator objective to generate a group of focused laser beams that can be utilized as the scale for measurement of an angular displacement of the target. By detecting the change in peak frequency in optical spectra obtained by the photodetector, a small angular displacement can be measured. In this paper, as the first step of research, a prototype optical setup is developed, and some basic experiments are carried out to demonstrate the feasibility of the proposed method for measurement of angular displacement.