Rooney, 26, previously captained England only once before in a friendly defeat over Brazil in 2009, but the match against San Marino will be his first competitive match as skipper.
"It's a great honour, it's something I'm really proud of," Rooney said during the pre-match press conference on Thursday.
"It's a big challenge for myself, I'm really looking forward to it and excited and hopefully we can cap the day off with a good victory," he said.
The Manchester United striker will aim to become the fifth highest goal-scorer for his country as England eye a goal fest at Wembley against a side ranked 207.
Rooney is currently on 29 goals for England and two more goals would lift him to fifth spot above the likes of Alan Shearer, Nat Lofthouse and Tom Finney, who have all scored 30 goals for England.
However, Rooney feels it's a great opportunity for his side to increase their goal difference before Tuesday's away clash against Poland.
"Obviously, the result is more important but it's an opportunity for us to try and get a few goals," Rooney said.
"We have to make sure we don't take them too lightly and we don't relax during the game.
"We have to forget they are ranked 207th, focus on ourselves, try and play the football we've been trying to do," he added.
Liverpool veteran Steven Gerrard is expected to retain the armband as he returns after suspension against Poland on Tuesday.