Is there an index tracking US hedge fund performance?

if there is such an index, is there any related etf or index mutual fund tracking this index?

Barclay's computes an index of the performance of all the hedge funds in its database. There are references to other such indexes on the web, but Barclay's is a very well known company, so their's is probably pretty good. I don't find any references to an ETF or mutual fund that tracks such an index

There is no such index because that information is not available. A firm such as (Barclays) can only track their own funds or funds that disclose their performance. However, the overwhelming majority of hedge funds do not disclose performance to anyone other than their shareholders. Essentially hedge funds are not public, so this information doesn't have to be reported to the SEC or anyone.

There are a lot of incentives for hedge funds to not disclose their performance. Primarily keeping performance records private keeps their holdings private. While one may not discern individual positions from tracked performance, inferences could be made about general exposure.

You much question any statistical data on hegde funds because it will largely be estimations based on a small sampling pool if not almost entirely hear-say.