We consider an asymmetric 0-pi Josephson junction consisting of 0 and pi regions of different lengths L_0 and L_pi. As predicted earlier this system can be described by an effective sine-Gordon equation for the spatially averaged phase so that the effective current-phase relation of this system includes a negative second harmonic. If its amplitude is large enough, the ground state of the junction is doubly degenerate. The phase shift depends on the amplitudes of the first and second harmonics. We study the behavior of such a junction in an applied magnetic field H and demonstrate that H induces an additional term proportional to H in the effective current-phase relation. This results in a non-trivial ground state tunable by magnetic field. The dependence of the critical current on H allows for revealing the ground state experimentally.