1540s, "natural head of hair" (a sense now obsolete), from French perruque (late 15c.), which is from Italian perrucca "head of hair, wig," a word of uncertain origin; supposed by some to be connected to Latin pilus "hair," "but the phonetic difficulties are considerable" [OED]. Meaning "periwig, artificial head of hair" (especially one having large and ample masses) is attested from 1560s. Compare periwig.
About the middle of the sixteenth century wearing the peruke became a fashion. Immense perukes with curls falling upon the shoulders were worn from about 1660 to 1725, and were then succeeded by smaller and more convenient forms, which had also existed contemporaneously with the former. As late as 1825 some old-fashioned people still wore perukes, and a reminiscence of them remains in Great Britain in the wigs of the Lord Chancellor, the Speaker of the House of Commons, judges, barristers, etc. [Century Dictionary]