Picasso, renowned as a tablecloth scribbler, once amused himself by painting a quick sketch across the bare back of a young woman seated on the beach at Cannes. The ''model'' was so overwhelmed that she wouldn't wash for months. But had she been wearing a T-shirt, the drawing would have been immortalized.
Today, an ingenious young American designer has capitalized on the idea with a collection of veritable ''art on your back'' - or rather ''front'' - of these T-shirts. Willi Smith, the black designer who founded WilliWear in 1976 and subsequently carried off such prestigious fashion laurels as the Coty Award in 1983 and the Cutty Sark Award this year, is promoting the T-shirts with drawings by 20 internationally known artists. This mobile ''gallery'' will go on exhibit at the end of September at the Galerie Viviane Esders, directly opposite the avant-garde Georges Pompidou Center here. Eventually the T-shirt will be available in various Paris boutiques priced around 200 francs ($2.25).