In the Middle Ages, bucklers were common armaments among both knights and common soldiers – even more so than shields. A buckler was less cumbersome and more agile than a larger shield and easier to carry about or wear on the hip.
-J. Clements (Sword and Buckler Fencing- Arma)
Another source claims that Mongolian Horse archers used a form of buckler.
This source
http://www.myarmoury.com/review_aa_ebuckler.html claims that bucklers were worn by archers, however it wasn't until the 15th century that this apparently became popular.
A third source says:
The medieval buckler was everywhere. Though often considered a defense of the merchant class, the buckler was used as both a training tool and a battlefield weapon by the knightly classes as well. In the later Middle Ages, most regular soldiers of a liveried army would carry a buckler, whether they were infantry, archers, halbardiers or gunners.
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http://www.mercwars.com/shieldtypes.shtml
They say this was from 1200-1500.
Combining all of the sources, it looks like it might have been possible for 13th century archers to carry bucklers on their hip, but I can't find a definitive source.