We show how to construct quantum stabilizer and subsystem codes from algebro-geometric toric codes extending the known construction of subsystem codes from cyclic codes and extending the construction of stabilizer codes from toric codes in an earlier work by one of the authors. Since algebrogeometric toric codes are higher dimensional extensions of cyclic codes, we obtain this way a new and rich source of quantum stabilizer and subsystem codes. We also show that the parameters of our quantum codes compare favorably with several of the existing quantum codes.