Composite films consisting of highly oriented boron nitride (BN) nanosheets in polysiloxane were fabricated without modifying the BN surface by applying a high magnetic field generated by a superconducting magnet. The hexagonal BN nanosheets were dispersed by sonication in a prepolymer mixture of polysiloxane. The homogeneous suspension was then cast on a polyamide spacer of microscale thickness and a magnetic field was applied before the mixture became crosslinked. The BN nanosheets in the polysiloxane were aligned with high anisotropy either parallel or perpendicular to the composite film plane depending on the magnetic flux direction. The fabricated composite films exhibited enhanced thermal conductivity by controlling the anisotropy of the BN nanosheets in the film. The mechanisms for rotation of BN nanosheets and heat diffusion across the composite film are discussed.