Magnetic early B-type stars are rare. Indirect indicators are needed to identify them before investing in time-intensive spectropolarimetric observations. We use the strongest indirect indicator of a magnetic field in B stars, which is periodic variability of ultraviolet (UV) stellar wind lines occurring symmetric about the approximate rest wavelength. Our aim is to identify probable magnetic candidates which would become targets for follow-up spectropolarimetry to search for a magnetic field. From the UV wind line variability the B1/B2V star sigma Lupi emerged as a new magnetic candidate star. AAT spectropolarimetric measurements with SEMPOL were obtained. The longitudinal component of the magnetic field integrated over the visible surface of the star was determined with the least- squares deconvolution method. The UV line variations of sigma Lupi are similar to what is known in magnetic B stars, but no periodicity could be determined. We detected a varying longitudinal magnetic field with amplitude of about 100G with error bars of typically 20G, which supports an oblique magnetic-rotator configuration. The equivalent width variations of the UV lines, the magnetic and the optical-line variations are consistent with the photometric period of 3.02d, which we identify with the rotation period of the star. Additional observations with ESPaDOnS attached to the CFHT confirmed this discovery, and allowed the determination of a precise magnetic period. Analysis revealed that sigma Lupi is a helium-strong star, with an enhanced nitrogen abundance and an underabundance of carbon, and has a chemically spotted surface. Conclusions. sigma Lupi is a magnetic oblique rotator, and is a He-strong star. Like in other magnetic B stars the UV wind emission appears to originate close to the magnetic equatorial plane, with maximum emission occurring when a magnetic pole points towards the Earth. The 3.01972+/-0.00043d magnetic rotation period is consistent with the photometric period, with maximum light corresponding to maximum magnetic field.