As the Roman Empire expanded, the state religion incorporated new deities and practices from all over the world: Bacchus, for example, was borrowed from the Greeks, while Isis came from Egypt, and Mithras from somewhere in the Middle East.
But were any of the state deities considered specifically Etruscan? (I'm interested in what the Romans thought about their deities' origin, rather than modern historians, so even if a connection is based on coincidence or folk etymology it's a valid answer.)
I think there probably are Roman deities that the Romans thought were worshipped by Etruscans. I'm less sure about the "specifically" Etruscan part. So far, I haven't seen a primary source that says anything clearly along the lines of "the Etruscans worshipped this god before the Romans did".
A lot of this stuff seems to be unclear, so this is just a provisional answer to get some possible starting points for later confirmation or disconfirmation. I may edit later to add primary sources. I wouldn't recommend accepting this post in its current state.
The best candidate I have found so far is Vertumnus:
Varro was convinced that Vortumnus was Etruscan, and a major god.6 [...] 6. Varro, De lingua latina V.46: "Ab eis [the Etruscans] dictus Vicus Tuscus, et ideo ibi Vortumnum stare, quod is deus Etruriae princeps"
(Wikipedia)
A less clear candidate is Summanus:
Pliny thought that he was of Etruscan origin, and one of the nine gods of thunder.3 Varro, however, lists Summanus among gods he considers of Sabine origin,"
(Wikipedia)
Footnote 3 cites Natural History 2.53. At first glance, I don't see how the cited passage confirms that Pliny thought that Summanus was of "Etruscan origin".
The Wikipedia article for Volturnus says that he was "originally an Etruscan god". I haven't checked the citations, so I don't know whether this is based on anything ancient, or on modern theories based on stuff like the form of the name.
