We present the first measurement of the gravitational quadrupole moment of the companion star of a spider pulsar, namely black widows and redbacks, using pulsar timing data for blackwidow PSR J2051-0827. To this end we have used a new timing model which is able to account for periastron precession caused by tidal and centrifugal deformations of the star as well as by general relativity. Simultaneously, the model allows for a time-varying component of the quadrupole moment, thus self-consistently accounting for the ill-understood orbital period variations observed in these systems. Our analysis results in the first unambiguous detection of orbital eccentricity in this system with e = 4.2 ± 0.1 · 10 −5 , together with a total precession of −68.6 +0.9 −0.5 deg/yr. We show that the variable quadrupole component is about 100 times smaller than the sum of the tidal and centrifugal components. We demonstrate how precise optical light curves of the companion star will allow to derive its apsidal motion constant from our results.