Step 1: Background on cheetahs in India.
- The Asiatic cheetah (\textit{Acinonyx jubatus venaticus}) once roamed India but was declared extinct in the wild in India by the 1950s.
- India has since launched a high-profile Cheetah Reintroduction Project, bringing African cheetahs from Namibia and South Africa.
Step 2: Evaluate other options.
Rusty spotted cat — native to India, still present (not extinct), no reintroduction program.
Jungle cat — widespread, not under reintroduction.
Jaguar — native to the Americas, not India.
Step 3: Conclude.
Only the cheetah has been the subject of an active and well-publicized reintroduction program in India (notably in Kuno National Park, Madhya Pradesh, starting 2022).
Final Answer:
\[
\boxed{(C)\ \text{Cheetah}}
\]