Search pattern containing forward slash using AWK

Yes, you can do

awk '$0~v' v="patt/ern"

Explanation

N.B.: extracted from comments, so upvote them too!

In awk dynamic regex and regex constant are not exactly same. The example in OP's question was regex constant you turned it into dynamic regex (see. Using Dynamic Regexps).

This may be OK for you:

kent$ echo "///aaa"|awk '/[/]/'
///aaa