All the information you require about Ram Theertha in Rameswaram:

The Ramanathaswamy temple, where Lord Rama is said to have worshipped Lord Shiva to remove the Brahmahati dosha brought on by murdering the Brahmin Ravana, is whence Rameswaram gets its name. Lord Shiva is referred to as the "Lord of Rama" or Rameswaram. Taking a dip in the 64 Theerthas, or sacred waters, is a significant aspect of visiting the Ramanathaswamy Temple. Of these, the Skanda Purana lists twenty-four as the most significant. Visit the Rama Theertha in Rameswaram if you wish to see these Theerthas. This is all the information you require about this location.

Gandhaman Parvatam, where the Rama Theertha in Rameswaram is situated, is rumored to have been visited by Rama during his journey to Sri Lanka. It is en route to Dhanushkodi, Lakshmana Theertha, and Sita Theertha.

What makes Ram Theertha unique?:

This tirtha is linked to numerous mythology and folklore. There are others who think that before departing for Sri Lanka, Lord Rama rested and had a bath at this pond. He peered out at the vastness of the ocean, trying to figure out how he was going to get to Ceylon. Some people think that Lord Rama cleansed himself of the sin of lying by taking a holy bath here.
Rama Padam, or Lord Rama's feet, is the subject of the Rama Theertha in Rameswaram. Some people think that this is where Vibhishana, the younger brother of Ravana, first met Rama.