The Welsh international scored four goals for the Gunners, which earned him the Premier League's Player of the Month award.
However, upon receiving the accolade, the 22-year-old said that he is "hoping for an even better October".
"Very happy to be named @premierleague Player of the Month for September. Hoping for an even better October," he wrote on the social networking site Twitter.
Ramsey has scored nine goals from his 13 outings for club and country so far this term.