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.
The former Newcastle United striker netted seven goals in 21 top-flight appearances on loan at West Ham last season, and Carroll hopes to continue that form next term.
“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.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news