Possibly, if he maxes out your credit limit on the card and don’t pay it down/off. But the sheer fact of sharing an account does not affect your score in any way. But cards that have been open longer and/or have high credit limits are the best to share. Ideally the account you share gets some usage, but gets payed off every month.
If your goal is to increase your son’s score, you would share the credit card account that is your oldest. Your son lacks Age of Account. Ideally the Average age of all your accounts is 10+ years. Your son can’t on his own have a 10 year old account, but if you share your account, now his average age of accounts shoots up. Another possibility is share an older account (perhaps not your oldest) that has a very high credit limit. A high credit limit may skyrocket a score.