  We theoretically investigate the critical bias current $j_c$ for a
superconducting (SC) ring in a magnetic field. Based on the Ginzburg-Landau
theory, we show that $j_c$ exhibits a Little-Parks (LP) oscillation as a
function of the magnetic flux passing through the ring, similarly to the LP
oscillation in the SC transition temperature. It is also found that for a
spin-triplet SC ring, the ${\bf d}$-vector rotates to yield a larger $j_c$,
forming a texture along the circumference of the ring. Experimental
implications of our result are discussed.
