The are two option to change calendar color.

First option:
If your iOS version is 5.0 or later, you can change calendar color in iCal, NOT AwesomeCalendar.

Open iCal(iPhone's built-in calendar app) and press edit calendar button. Then you can change calendar color.
If you change calendar color in iCal, changed color will automatically be applied to AwesomeCalendar.

Second option:
You can change calendar color in AwesomeCalendar Settings. "AwesomeCalendar Settings>Calendars & Reminders". But if you change calendar color in AwesomeCalendar settings, color doesn't sync with other devices, such as iPad. If you have several devices, first option is recommended.