The black and white on the new sconce go most likely to where the black and the white were connected from the old sconce. Absent a green or bare wire in the box or some sort of other ground (conduit or armored cable clamped to the box) you have nothing to connect the ground to.

If that is the case, you have three options:

Install it anyway leaving the ground disconnected provided it has no exposed metal on it.

Install it anyway but protect that circuit with a GFCI.

Run a ground wire to some accessible point of the grounding system.

Thanks ronnatale. I got a current tester and the red wire is indeed the hot one. So, I did as you suggest and hooked the red to black, black/white to white. The circuit does have a GFCI and I bent the bare wire so that it is touching the bracket for the light, which is screwed in to the box. I turned the current back on, and it all seems to be working correctly. Thank you for the advice!