The partially convertible rupee was at 62.26/27 to the dollar versus its close of 62.09/10 on Wednesday.
The U.S. central bank said it would reduce its monthly asset purchases by $10 billion, bringing them down to $75 billion. The taper will be equally split between mortgage-backed securities and Treasury bonds.
The currency is seen as less vulnerable than in the summer when it sold off on fears of a wide current account deficit.
The central bank has since added $34 billion to its reserves after opening two concessional forex swap facilities to draw inflows.