Step 1: Understand the question
We are asked to identify an Indian musician who has won the Oscar (Academy Award) two times. Step 2: Analyze achievements of each option
M.M. Keeravani won 1 Oscar for the song "Naatu Naatu" from the movie RRR in 2023.
Bhanu Athaiya was a costume designer, not a musician, and won 1 Oscar in 1983.
A.R. Rahman won 2 Oscars in 2009 for Slumdog Millionaire: one for Best Original Score and another for Best Original Song.
Resul Pookutty won 1 Oscar for Best Sound Mixing for Slumdog Millionaire in 2009. Step 3: Conclusion
A.R. Rahman is the only Indian musician listed who has won the Oscar award twice.