Aqaba is a costal tourist city, there are no rules that govern what you can and cannot wear in public, be advised that public nudity is prohibited by law.
women and men can wear casual and beach clothing in public, although it is advised that during the month of Ramadan some descrition is advised. Culturally it is frawned upon for men to be walking in the street bear chested or for ladies to be walking arounf in their bikini.
When entering a mosque also be advised that proper clothing is a must.