The F-35A has not yet done any trials/clearance to carry the B61-12 nuclear bomb. These are scheduled to be performed sometime between 2020-2022, though there is an argument going on as to when they are required - based in their role and the retirement of the currently assigned users.
Based on the different airframes previously cleared for carriage, such as the Jaguar, The any such clearance is likely to be more difficult politically than aerodynamically - particularly since the range of the F-35A would limit the targets to any German based F-35As to countries such as Poland, Hungary or the Baltic states......