Rotation invariant moments have attracted considerable interest in image processing and pattern recognition. We present a new category of rotation invariant moments derived from Slepian functions, which are initially created for the separation of variables in solving Helmholtz equations. Recent studies have shown that Slepian functions excel in local approximation compared to other basis functions. Inspired by their exceptional approximation capabilities, we construct Slepian-based moments in this work. We show their rotation invariance property and present experimental results that highlight their effectiveness in classification tasks on real data. The proposed rotation invariant moments are robust to noise in facial expression classification.