In this Letter, the authors introduce a fractional angular number transform (FrANT). The new transform corresponds to a finite field version of the complex‐valued discrete fractional angular transform and, therefore, its computation requires integer arithmetic only. Differently from other number‐theoretic transforms, the possible lengths of an FrANT do not depend on the algebraic structure where it is defined. This provides more flexibility regarding the application of the transform in communications, cryptography and error correcting codes, for instance.