Of course you can include your parents in your wedding ceremony. Pretty much you can do anything you would like in your ceremony, apart from changing the legal wording.
The best way to include you parents is to have both of them walk you down the aisle. If this idea does not sit right with you, then you can just have one of them walk you down the aisle.
Another way you can include them is to have them formally “give you away” during the ceremony. The way we do this is I ask “Who bring this woman to be married to this man?” Both parents then say “We do.”
You could also give you parents a gift during the wedding ceremony and acknowledge all of their love and sacrifice over the years.
Lastly, you could include them in a unity candle lighting.
There are many ways to bring you parents into the ceremony, these are simply a few examples.