The early access program was being offered to Apple employees for the symbolic price of 49¢ per month, with a one-month free trial, until the end of the early access period, which was said to be when iOS 13 ships to customers.
Today, I was able to get information about the price of an Apple Arcade subscription to customers. This information is available in one of the APIs used by the App Store app. According to a promotional message found in the service, the price for Apple Arcade will be $4.99 / month, including a one-month free trial. As Apple previously announced, the service will allow access to all members in a Family Sharing account.
Since the price has not been officially announced yet, it’s possible that it will change before the announcement, which is likely going to on September 10, when Apple is expected to hold a special event to announce new iPhones.