From observations collected with the ESPaDOnS and NARVAL spectropolarimeters, we report the detection of Zeeman signatures on the classical T Tauri star (cTTS) BP Tau. Circular polarization signatures in photospheric lines and in narrow emission lines tracing magnetospheric accretion are monitored throughout most of the rotation cycle of BP Tau at two different epochs in 2006. We observe that rotational modulation dominates the temporal variations of both unpolarized and circularly polarized spectral proxies tracing the photosphere and the footpoints of accretion funnels.From the complete data sets at each epoch, we reconstruct the large-scale magnetic topology and the location of accretion spots at the surface of BP Tau using tomographic imaging. We find that the field of BP Tau involves a 1.2 kG dipole and 1.6 kG octupole, both slightly tilted with respect to the rotation axis. Accretion spots coincide with the two main magnetic poles at high latitudes and overlap with dark photospheric spots; they cover about 2 per cent of the stellar surface. The strong mainly axisymmetric poloidal field of BP Tau is very reminiscent of magnetic topologies of fully convective dwarfs. It suggests that magnetic fields of fully convective cTTSs such as BP Tau are likely not fossil remants, but rather result from vigorous dynamo action operating within the bulk of their convective zones.Preliminary modelling suggests that the magnetosphere of BP Tau extends to distances of at least 4R* to ensure that accretion spots are located at high latitudes, and is not blown open close to the surface by a putative stellar wind. It apparently succeeds in coupling to the accretion disc as far out as the corotation radius, and could possibly explain the slow rotation of BP Tau.