Either the word puma or the word lion would fit that description.
Lynx, or for a very big cat consider the Puma or the Lion.
The girl stroked the tawny fur of her old cat as she gazed up at the brilliant full moon, oblivious of everything around her.
cougar
A large, tawny colored cat, males with a mane of hair, somewhat smaller than a tiger.
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There are many felines that have a tawny brown coloration. Domesticated cats can come in that color but, if looker for a larger feline then Cougars and African Lions are that color.
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