For any reasonable risk, the answer is no. Virtually all tumors are non-transmissible under normal (non-laboratory) circumstances (three exceptions, discussed below, none in humans), so you could not possibly get the cancer the animal had.
However some cancers arise because of environmental factors which may still be present in the animal. For example, an animal exposed to polychlorinated biphenyls (PCBs) would be at a higher risk of developing cancer, and PCBs also tend to stay around in the animal for some time. It is at least possible that environmental exposure which gave the animal cancer is still around to increase the risk to you. In general, this is probably a pretty low risk from any one instance of eating a tumorous animal. However if you were to eat animals which were routinely contaminated with something carcinogenic, it could become a problem.
A similar story could be told about oncoviruses, that is viruses which can cause tumors or cancer. However all the oncoviruses known to date are restricted to humans. Further, if there were an hitherto unknown oncovirus which caused the tumor in the animal and still could cause an infection and neoplasm in humans, it would have to survive cooking and consumption. This route seems improbable.
The least probable route would be a directly transmissible tumor. There are two such tumors known: Tasmanian devil facial tumor disease and canine transmissible venereal tumor. A third variety was discovered this year (Metzger 2015), which is found in clams. None affects humans. Further, the chances of such a disease being able to transmit across species seems very improbable. Finally, food preparation is almost certain to kill off the tumor cells.
In summary, it is very improbable that eating an animal which had a neoplasm would pose any risk.