According to Valmiki Ramayana, Lord Rama was born in Punarvasu nakshatra. The first three Padas of Punarvasu lie in Mithuna rashi and the last Pada lies in Karkataka rashi. Valmiki does not mention the Pada in which Lord Rama was born which is crucial in deciding His birth rashi. In which rashi was Lord Rama born?
Birth rashi of Lord Rama is mentioned in Bala Kanda of Ramayana as Punarvasu as Rashi is decided by Moon Sign in a horoscope.
18:8,9,10,11 On completion of the ritual six seasons have passed by and then in the twelfth month, on the ninth day of chaitra month [April-May,] when the presiding deity of ruling star of the day is Aditi, where the ruling star of day is punarvasu, the asterism is in the ascendant, and when five of the nine planets viz., Sun, Mars, Jupiter, Saturn, and Venus are at their highest position, when Jupiter with Moon is ascendant in Cancer, and when day is advancing, then Queen Kausalya gave birth to a son with all the divine attributes like lotus-red eyes, lengthy arms, roseate lips, voice like drumbeat, and who took birth to delight the Ikshwaku dynasty, who is adored by all the worlds, and who is the greatly blessed epitome of Vishnu, namely Rama.
Punarvasu 4th pada lies in Cancer in the house where Jupiter also exalts, while first three pada of Punarvasu lie in Gemini.
Lord Rama's Horoscope
Sun, Mars, Jupiter, Saturn and Venus are exalted, Mercury Neechbhanga with Moon in Punarvasu-4 as Rashi sign as well as ascendant lord
The birth of Sri Raama was stated as follows;
ततो यज्ञे समाप्ते तु ऋतूनाम् षट् समत्ययुः | ततः च द्वादशे मासे चैत्रे नावमिके तिथौ || १-१८-८ नक्क्षत्रे अदिति दैवत्ये स्व उच्छ संस्थेषु पंचसु | ग्रहेषु कर्कटे लग्ने वाक्पता इंदुना सह || १-१८-९
On completion of the ritual, six seasons have passed by; then in the twelfth month, i.e., in chaitra mAsa, and on the ninth day of that chaitra month [April-May], when it is punarvasu nakshatra yukta navamI tithi, i.e., when the ruling star of that ninth day is punarvasu, for which Aditi is the presiding deity; and when five of the nine planets - (sUrya, kuja, guru, shukra, shani) are in ucCha sthAna-s, namely, when those planets are in ascension in their respective houses - meSha, makara, karkaTa, mIna, tula - rAshI-s; and when chandra yukta guru, karkaTa lagne - Jupiter in conjuction with Moon is ascendant in Cancer, and when day is advancing
So Jupiter alongwith Moon was in Cancer, which was also the ascendant.
Hence, Sri Raama took birth in Punarvasu - 4 pada, which will fall in Cancer or Karkataka rashi.