Is it possible for the radiation therapy for one cancer to give me another form of cancer?

Yes. It is possible but statistically low. The benefits for the cancer you are treating will far outweigh this risk. However any unnecessary risk should not be taken if for example radiation has no known benefit for the condition being treated.
Very low chance. It is possible for radiation therapy for one cancer to lead to a second cancer however this risk is about 5 excess cancers per 1000 patients treated by 15 years after diagnosis (gonzalez a et al. Lancet oncology. Vol 12, issue 4, 2011).
Rare but possible. Like anything there are good and bad sides. For most, the advantages of treating a known cancer far outweigh the rare risks of an induced cancer usually at least 10-15 years later. One well documented area though is women who receive mantle radiation for hodgkins. There is an increase in breast cancer risk starting 10-15 yrs later which warrants high risk surveillance including screening bmri.

Related Questions

Can radiation therapy mutate one form of cancer into a more aggressive form?

Yes. In the way you asked the question it can. It depends on the dose. Low dose exposures can allow cells to survive and this could happen. In the treatment with radiation the cancer is treated to levels that are designed to kill the cells and therefore mutation to more aggression is not likely. There are many resistance cancers however and it is more likely the cancer is already aggressive. Read more...
Typically, no. Radiation can cause cells to become precancerous, and potentially develop into a cancer ("secondary malignancy.") pre-existing cancers do not generally mutate into more aggressive grades after radiation exposure. Read more...