Carroll has endured a tough time since joining the Hammers on loan from Liverpool, but he terrorised the West Bromwich Albion defence on Saturday and scored two goals in their 3-1 win.
A bullet header and an exquisite volley showed off his undoubted quality and he hopes to continue impressing to further his claims in Hodgson's squad for summer friendlies with the Republic of Ireland and Brazil.
"I hope to play in every game for England but I've haven't been picked, so I've just got to work hard here at West Ham and hopefully I'll be involved next time," Carroll said.
"I was putting myself about and got two goals, so that's what I like to think I'm about. Obviously I like to score goals, so getting two shows that I've got it.
"I'm feeling good with the lads and everyone is coming together and we're playing well at home.
"It was a great win. The lads worked hard and I got my two goals and we got the three points, so it was a great day."