Weakly interacting massive particles (WIMPs) are among the favored candidates for cold dark matter in the universe. The phenomenology of supersymmetric WIMPs has been quite developed during recent years. However, there are other possibilities which have not been discussed as much. One example is a right-handed massive neutrino, which has recently been proposed in the context of a version of the Zee model for massive neutrinos. This TeV-scale, leptonic WIMP (or LIMP, for short) may at first sight appear to be essentially undetectable. However, we point out that the radiatively induced annihilation rate into leptons and photons is bound to be substantial, and provides a conspicuous gamma-ray signature for annihilations in the galactic halo. This gives a window of opportunity for AirČerenkov Telescopes with ability to observe the galactic center, such as the HESS and CANGAROO arrays, and also for the GLAST space telescope. In addition, the contribution to the positron cosmic ray flux is in principle detectable, but this would require very strong local density enhancements in the dark matter halo distribution.PACS numbers: 95.35.+d, 14.60.St, 95.85.Pw, 95.85.Ry, 98.70.Rz