Lord Shiva has been worshipped in Linga form from time beginning as described in answer here. Among the Lingas there are 12 Jyotirlingas which are of special importance.
Mahatmya of 12 Jyotirlingas is described in Koti Rudra Samhita of Shiva Purana in the chapter "Dwadash Jyotirlinga Mahatmya". It states:
सौराष्ट्रे सोमनाथं च श्री शैले मल्लिकार्जुनम् ।
उज्जयिन्यां महाकालमोंकारे परमेश्वरम् ।।
केदारं हिमवत्पृष्ठे डाकिन्यां भीमशङ्करम् ।
वाराणास्यां च विश्वेशं त्रयम्बकं गौतमीतटे ।।
वैद्यनाथं चिताभूमौ नागेशं दारुकावने ।
सेतुबन्धे तु रामेशं घुश्मेशं च शिवालये ।।
द्वादशैतानि नामानि प्रात्यस्त्थाय यः पठेत् ।
सर्वपापविनिर्मुक्तं सर्वसिद्धिफलं लभेत् ।।
Somanath in Saurashtra, Mallikarjuna in Shri Saile, Mahakala in Ujjaiyana and Parameshawara also manifested as Omkara. Kedara in Himavat and Bhima Shankara in Dakinya. Vishewaswara in Varanasi and Trayambaka in side of Gautami. Vaidyanath in ChitaBhumi and Nageshwara in forest of Daruka. Rameshwara in Setubandha and Ghusmeshwara in Shivalaya. These name of 12 Jyotirlingas who recites in morning, he gets freed from all sins and is eligible to get all Siddhis.
There are twelve Jyotirlingas mentioned in the similar popular verse.
Saurāṣṭre Somanāthaṃ ca Śrīśaile Mallikārjunam
Ujjayinyāṃ Mahākālam Omkāram Mamleśhwaram
Paraly Vaidyanāthaṃ cha Ḍākinyāṃ Bhīmaśhaṅkaram
Setubandhe tu Rāmeśaṃ Nāgeśhaṃ Dārukāvane
Vārāṇasyāṃ tu Viśveśaṃ Tryambakaṃ Gautamītaṭe
Himālaye tu Kedāraṃ Ghuśmeśaṃ ca Śivālaye
etāni jyotirliṅgāni sāyaṃ prātaḥ paṭhennaraḥ
saptajanmakṛtaṃ pāpaṃ smaraṇena vinaśyati
I have already asked a question about Somanath What is the story of Somanath Jyotirlinga? and Mallikarjun What is the story of Mallikarjuna Jyotirlinga? and Mahakaleshwar What is the story of Mahakaleshwar Jyotirlinga? and Omkareshwar What is the story of Omkareshwar Jyotirlinga? and Vaidyanath What is the story of Vaidyanath Jyotirlinga? and Bheemshankar What is the story of Bheemshankar Jyotirlinga?. Now I want to know the story of Rameshwaram Jyotirling.
Please mention the scriptural reference.
Rameshwaram temple is situated in Ramanathapuram, Tamil Nadu.
By Ssriram mt - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=48384927