Yes you can do that but you need your server for the same
Steps for that:

1. Create your own deeplink which point to your webpage/backend

2. On your server, store the referralCode and associate it with metadata, So that when someone visit link, via cookie, we can send request and redirect to appstore. (Half way you're done)

Now question for how can use the referred code which user already pasted:

There are 2 ways:
1. save it using UIPasteboard, Check if its fit in your scenario
2. Prompt referred code view when 1st lanuch app, like now a days eCommerce apps do.