Why is our solar system "tipped" about 63° with respect to the plane of our galaxy?

What you could think at first, regarding the orientation of any planetary system, is that it should be roughly in the plane of the galaxy, simply by angular momentum conservation.

But, when you take a look at observations, you see that protoplanetary disks orientation is not what you would expect, with no preferential orientation (protoplanetary disks are embryo of planetary systems, that makes them interesting). In the following figure, the orientation corresponds to the inclination between the line of sight and the rotation axis of the disk.

Why there is this distribution of orientation?

The angular momentum scenario is nice but far to simple: star formation occurs in gas clouds in the interstellar medium, and these clouds are known to be turbulent (Larson, 1981). Turbulence simply disrupts the gas, and is dominent over the global angular momentum of the cloud. Actually, you can even test that with numerical simulations of star formation: put an initial angular momentum consistent with observations, and some turbulence (subsonic or slightly supersonic, also in accordance to observations), and you will get a misalignement of the rotation axis, due to turbulence.