  We calculate the deflection of a light ray caused by the gravitational field
of a cosmic string loop in the weak field limit and reduce the problem to a
single quadrature over a time slice of the loop's world sheet. We then apply
this formalism to the problem of gravitational lensing by cosmic string loops.
In particular, we find an analytic solution for the special case of a circular
loop perpendicular to the optical axis. As examples of more complicated loops,
we consider two loops with higher frequency Fourier modes. The numerical
analysis illustrates the general features of loop lenses. Our estimates, using
typical parameters for GUT scale loops, show that the stringy nature of loop
lenses can be observed for lensing systems involving high redshift galaxies ($z
\sim 2$), and we suggest that gravitational lensing can confirm the existence
of GUT scale strings if they are the seeds for large scale structure formation.
