In this study, ultrafiltration membranes were developed via a nonsolvent-induced phase separation method for the removal of asphaltenes from crude oil. Polyacrylonitrile (PAN) and acrylonitrile copolymers with acrylic acid were used as membrane materials. Copolymerizing acrylonitrile with acrylic acid resulted in an improvement in the fouling resistance of the membranes. The addition of 10% of acrylic acid to the polymer chain decreases the water contact angle from 71° to 43°, reducing both the total fouling and irreversible fouling compared to membranes made from a PAN homopolymer. The obtained membranes with a pore size of 32–55 nm demonstrated a pure toluene permeance of 84.8–130.4 L/(m2·h·bar) and asphaltene rejection from oil/toluene solutions (100 g/L) of 33–95%. An analysis of the asphaltene rejection values revealed that the addition of acrylic acid increases the rejection values in comparison to PAN membranes with the same pore size. Our results suggest that the acrylonitrile–acrylic acid copolymer ultrafiltration membranes have promising potential for the efficient removal of asphaltenes from crude oil.