How can I paint my oven door without it scratching off

They sell appliance paint. Make sure you get the one that's ok with hot temps. Prob is I did my fridge about nine months ago and it looks great everywhere except handles where it is starting to show wear.

Big box stores, hardware stores and some Walmart stores carry spray paint that is specifically for painting appliances that get hot. It works really well, but unless you can take your oven outside to paint make sure you cover everything else around it to prevent overspray issues. I think the brand I used was Rust-Oleum.

Is there glass in the door

Use the right paint! You need to look for appliance paint.