We consider a superfluid of trapped fermionic atoms and study the single vo
rtex solution in the Ginzburg-Landau regime. We define simple analytical es
timates for the main characteristics of the system, such as the vortex core
size, temperature regimes for the existence of a vortex, and the effects o
f rotation and interactions with normal fermions. The parameter dependence
of the vortex core size (healing length) is found to be essentially differe
nt from that of the healing length in metallic superconductors or in trappe
d atomic Bose-Einstein condensation in the Thomas-Fermi limit. This is an i
ndication of the importance of the confining geometry for the properties of
fermionic superfluids.