The scales of Raga Shivaranjani are as follows :
Aarohanam (Ascending) : S R2 G2 P D2 S’
Avarohanam (Descending) : S’ D2 P G2 R2 S
Shivaranjani is a janya raga, derived from Kharaharapriya (see below), 22th on the Melakarta scale.
The mood of this raga is from melancholy to deep anguish. It is a fairly recent entrant to Carnatic music and is used for ‘lighter’ pieces near the end of the concert. I am familiar with only a few compositions – Tarunamidaiya and Andavan Anbe, both by Papanasam Sivan and Bombay Jayashri’s rendition of Kuzhalosai Ketkudamma by Sudhananda Bharathi (originally in Khamas). I associate this raga more easily with film music like Tere Mere Beech Mein from Ek Duje Ke Liye, Mere Naina Sanwan Badho from Mehbooba and Jane Kahan Gaye Woh Din from Mera Naam Joker.
A beautiful variant is Mishra Shivaranjani in which the extra note G3 is infrequently used, lending even more pathos and beauty to this raga. Good examples are the Thillanas composed by Lalgudi Jayaraman and Maharajapuram Santhanam.
Tamil speakers may enjoy the video below by Charulata Mani in her Isai Payanam series. She talks about Shivaranjani and Nilamani, very similar ragas.
Note : The 12 notes in the octave are named as below. Please note that C is used as Sa for the sake of simplicity as the scale is relative in Carnatic Music. Also note that the scales paint only a superficial picture of the raga as the gamakas(ornamentations) are a very important part of a raga.
Music To My Ears 
Really helpful
Thank you!