My cycle was every 29 days, without fail, prior to meds. Now? Maybe every 26, 27, 28...but never 29. Weird, but there it is.
My own experience with levothyroxine-no change. However I'm also on birth control.
Do you mean your menstrual cycle? Is it unusually short, like 21 days? I am not on meds, but I've found it curious that I went from 30-33 day cycles to <24 days in the last year, the same time I've been having odd physical symptoms that are likely related to my thyroid.
Certainly an interesting idea though.