WASHINGTON, July 6 (Reuters) - A Republican entrepreneur seeking to push his party to fight climate change and support clean energy said on Sunday he has given his first big campaign gift to Senator Kelly Ayotte of New Hampshire.

Jay Faison, an audio tech executive who this year set up Clearpath, a foundation dedicated to explaining to Republicans the science behind climate change and business opportunities to fight carbon emissions, said he had given $500,000 to Ayotte, who was elected to the Senate in 2010.

Faison, who gave the money to Ayotte's super PAC as a personal donation, said he hoped politicians like her would help push Republicans to adopt a new approach to climate change that "is really going to help the party in the end."

Ayotte has shown a tendency to split with fellow Republicans on climate issues.

When Republican leaders in the Senate made passing a bill to approve the Keystone XL oil pipeline from Canada their top priority early this year, Ayotte voted for the bill, like all of her fellow party members in the 100-member chamber.

But she was one of five Republicans to also vote for an amendment to the Keystone bill introduced by Democrat Brian Schatz declaring that humans are a significant cause of climate change. The measure, which ultimately failed because it did not have 60 votes, was meant to force Republicans to show their hand on climate.

Ayotte has a lifetime voting rating of 23 from the League of Conservation Voters, a political advocacy group. That is well below the rating of Senator Susan Collins of Maine, a fellow Republican who got a score of 65, but who is not running for re-election in 2016.

Ayotte has gradually warmed to climate issues. In 2010, she said she did not think the scientific evidence was conclusive that humans were causing climate change.

However, Faison said he was not worried by such wavering from five years. "It's hard to be perfect as a Republican on this issue," he said.

This year Faison has also given $100,000 to 2016 Republican presidential candidates Senator Lindsey Graham's super PAC, and $50,000 to Jeb Bush's super PAC. (Editing by Paul Tait)