When did men start wearing ruffled shirts?

That depends on what you mean by a "ruffled shirt." Men - almost exclusively among the landed aristocracy - wore ruffled collars and cuffs throughout the 16th Century. A man's shirt at the time was considered an undergarment and not meant to be seen. It wasn't until the middle of the following century that men started exposing their shirt-fronts, and what was seen underneath their waistcoats was often ruffled. Well-to-do men wore ruffled shirts as a matter of course from then until the middle of the 19th Century, and with evening wear into the 20th. Over time, menswear has gotten progressively simpler, and the ruffled evening shirt was all but extinct by the end of World War I.

Men's ruffled shirts enjoyed a brief revival in the 1960s and 1970s. It is all but impossible to find one today.