Could I add new ACT score after early admission application?

My current ACT score is not that great, so I plan on taking the one in October. However, I will not get the grade back for the test until after I apply early action. Is there a possibility I could change/give new test scores after I apply?

Your target school will clearly spell out what are the last testing dates for which scores can be included in your EA app. There lies your answer, not here. Good luck

Many schools (though not all) say you can send scores after the deadline, but they may not be read.
This doesn’t mean you shouldn’t take the act again, though, because if you are deferred you can send in the higher score.

Visit each school’s admissions page. Almost all schools are very clear on latest test dates for ED, EA and RD.