Bernstein-Frenkel-Khovanov, Sussan, etc have constructed categorifications of various tensor products representations of sl_m using singular blocks of category O for sl_n. Here we construct a positive characteristic analogue using blocks of representations of sl_m in positive characteristic, with a nilpotent Frobenius character, and singular Harish-Chandra characters. In some cases they admit graded lifts, and are equivalent to a geometric categorification constructed by Cautis-Kamnitzer-Licata using coherent sheaves on co-tangent bundles to partial flag varieties (via equivalences due to Riche and Bezrukavnikov-Mirkovic-Rumynin). This is joint work with Gufang Zhao.