Is there a blood test that can indicate if someone has cancer?

Yes: Yes, but it is not that straightforward. It is most appropriately used when you know somebody has cancer, the cancer has been treated, and you are looking for regrowth of the cancer. Using the tests any other way can be very misleading. It also depends on what kind of cancer you have (ldh, afp, thyroglobulin, cea, ca19-9, ca 125, and chromogranin are all examples).