What is the name of the Power Rangers series that adapted 'Samurai Sentai Shinkenger'?

The Power Rangers series that adapted Samurai Sentai Shinkenger is Power Rangers Samurai.

Power Rangers Samurai premiered in 2011 and became the seventeenth entry in the American franchise. Its story follows a team of Rangers trained in samurai traditions who defend Earth from the Nighloks, using symbol-powered weapons, folding Zords, and the Samurai Megazord.

The series uses costumes, action footage, props, and story concepts from Toei's Japanese production Samurai Sentai Shinkenger, which aired in Japan from 2009 to 2010. This was not a loose title reference: the American production was a direct adaptation reshaped for English-speaking audiences and Nickelodeon's programming style.

A frequent source of confusion is Power Rangers Super Samurai. Super Samurai is the follow-up season that continues the Samurai storyline, rather than the original adaptation's primary title. Power Rangers Megaforce and Super Megaforce adapted different Super Sentai material, while RPM was based on Engine Sentai Go-onger.