We report an experimental investigation of the magnetic field effect (MFE) in polymer bulk heterojunction devices at temperatures below 10 K using photocarrier extraction by linearly increasing voltages. The examined devices were composed of an active layer of poly(3-hexylthiophene) and [6,6]-phenyl-C61-butyric acid methyl ester. In the experiments, the delay time (td) dependence of the MFE was investigated in detail. For td < 80 μs, a positive MFE was observed in the field region B < 0.1 T and a negative MFE was observed for B > 0.2 T. For td > 8 ms, only a positive MFE proportional to B2 was observed. For the photocurrent pulse detected immediately after light irradiation, the MFE was negligibly small. In a high magnetic field of 15 T, a significant MFE exceeding 80% was observed at 1.8 K for td = 800 ms. We discuss the results based on a model of triplet-singlet (or singlet-triplet) conversion in the magnetic field and estimate the exchange integral for the charge-transfer exciton in this photovoltaic cell.