A disordered stress-free granular packing can be jammed, transformed into a mechanically rigid structure, by increasing the density of particles or by applying shear deformation. The jamming behavior of systems made of 2D circular discs has been investigated in detail, but very little is known about jamming for non-spherical particles, and particularly, non-convex particles. Here, we perform an experimental study on jamming by compression of a system of quasi-2D granular crosses made of photo-elastic crosses. We measure the pressure evolution during cyclic compression and decompression. The Jamming packing fraction of these quasi-2D granular crosses is φ J ≈ 0.475, which is much smaller than the value φ J ≈ 0.84 for-2D granular disks. The packing fraction shifts systematically to higher values under compressive cycling, corresponding to systematic shifts in the stress-strain response curves. Associated with these shifts are rotations of the crosses, with minimal changes in their centers of mass.