The normal word for "duty" in Latin isn't ius, but officium, and it's well attested for this meaning from Plautus to Suetonius (and later), in prose and poetry alike. Cicero's De Officiis is always translated as On Duties. Might be easier to just post the Lewis & Short definition in full:
II. In gen., an obligatory service, an obligation, duty, function, part, office (so most freq. in prose and poetry of all periods): “nulla vitae pars neque publicis neque privatis neque forensibus neque domesticis in rebus, neque si tecum agas quid, neque, si cum altero contrahas, vacare oflicio potest: in eoque et colendo sita vitae est honestas omnis et in neglegendo turpitudo, etc.,” Cic. Off. 1, 2, 4 sq.: perfectum officium rectum opinor vocemus, quod Graeci κατόρθωμα: hoc autem commune καθῆκον vocant, id. ib. 1, 3, 8; “an id doles, quia illi suum officium non colunt, quom tu tuum facis?” Plaut. Stich. 1, 1, 34; id. ib. 1, 1, 39; id. Pers. 4, 4, 66: “meminisse officium suum,” to remember one's duty, id. Trin. 3, 2, 71.—Also, subject., a sense of duty: “si quis aegre ferat nihil in se esse virtutis, nihil officii, etc.,” Cic. Tusc. 4, 28, 61: “quicquid in eum judicii officiique contuleris,” id. Fam. 10, 1 fin.: “intellegere, utrum apud eos pudor atque officium an timor valeret,” Caes. B. G. 1, 40, 14: “suum facere,” to do one's duty, Ter. Ad. 1, 1, 44: “omnibus officiis amicitiae servatis,” observe all the obligations of friendship, Cic. Fam. 5, 17, 3: “exsequi,” id. Att. 3, 15, 4: “fungi officio,” id. Fam. 3, 8, 3: “satisfacere officio,” to perform, id. Div. in Caecil. 14, 47: “officium suum deserere,” to disregard one's duty, not perform it, id. Off. 1, 9, 28: “discedere ab officio,” id. ib. 1, 10, 32: “deesse officio suo,” id. Fam. 7, 3, 1: “officii duxit,” considered it his duty, Suet. Tib. 11.—Of animals: “canes funguntur officiis luporum,” act the part of, Auct. Her. 4, 34, 46.—Of things: “neque pes neque mens satis suum officium facit,” Ter. Eun. 4, 5, 3: officium corporis, the function or property of a body, Lucr. 1, 336 and 362.
Ius, on the other hand, doesn't really mean "duty", and although L&S says so, they don't give very many examples of it. It rather means "right" or "law." When Cicero talks about natural or divine laws, the sort of "laws" that all people should follow regardless of human laws, he speaks of ius.
In that sense, it's a "duty" in that we must obey it. It's not really "duty" in the sense of "civic duty" or "duties of the magistrate", both of which would use officium instead.
