Valmiki Ramayana does not specify to the fact directly.
But it states Rama worshipped Shiva at Rameswaram.
That Rama installed a Shiva lingam is referred to in Adhyatma Ramayana,Shiva Purana,Linga Purana,Skanda Purana, Padma Purana,Ramacharitamanas by Tulsidas and Shiva Daridra
