Here's a one-line conversion using Lua, similar to blueyed's answer except with all the RFC 3986 Unreserved Characters left unencoded (like this answer):
url=$(echo 'print((arg[1]:gsub("([^%w%-%.%_%~])",function(c)return("%%%02X"):format(c:byte())end)))' | lua - "$1")
Additionally, you may need to ensure that newlines in your string are converted from LF to CRLF, in which case you can insert a gsub("\r?\n", "\r\n")
in the chain before the percent-encoding.
Here's a variant that, in the non-standard style of application/x-www-form-urlencoded, does that newline normalization, as well as encoding spaces as '+' instead of '%20' (which could probably be added to the Perl snippet using a similar technique).
url=$(echo 'print((arg[1]:gsub("\r?\n", "\r\n"):gsub("([^%w%-%.%_%~ ]))",function(c)return("%%%02X"):format(c:byte())end):gsub(" ","+"))' | lua - "$1")