The 24-year-old signed a six-year deal with the Hammers after completing a reported £16m move to Upton Park from Liverpool on Wednesday.
Carroll was part of Roy Hodgson’s 23-man travelling party for Euro 2012, scoring against Sweden, but has struggled to hold down a squad spot.
“My aim is keeping fit, scoring goals and performing every week,” Carroll told the Daily Mail.
“If I do that I’ll hopefully get in the England team. It’s always important to play football for your country. If I play well and keep fit, I’m going to be playing every week. If it comes, England will come.
“Sam’s [Allardyce] a great manager. It’s always good when you’ve got somebody behind you. He gives me confidence to show what I am about.”
The England international scored just six goals in 44 Premier League appearances for Liverpool before swapping Anfield for the east London outfit.
Get enhanced odds of 18/1 on Andy Murray to win Wimbledon or 10/1 on Novak Djokovic when you open a Paddy Power account.