As kev has pointed out, Special Relativity accounts for the Sagnac effect. It is probably relevant to add that, although some authors refer to the effect as being a "Special Relativity effect" per se, in his mathpages Kevin Brown points out that actually it is a classical effect, because it doesn't involve second order metric effects on lengths, times, etc. that more properly call for the designation, "relativistic." Certainly, Sagnac himself saw it as a classical effect, explicable in terms of the ether paradigm.
Also relevant is that the Sagnac effect is but part of the more general "problem" of rotating reference frames. Although many regard this as not really a problem, being accounted for by Einstein's theories, among some physicists, including Klauber, the proper relativistic interpretation is a lively topic of debate. (See the book, Relativity in Rotating Frames, Eds., G Rizzi and M. L. Ruggiero).