You can certainly put urls into a text/plain email. It helps if your urls aren't terribly long and don't have characters that are questionable in urls.
w3c suggests surrounding them with angle brackets [1], but I can't find a source that makes more than a suggestion. By reports, some mail user agents, and some users will include the trailing > in the url they provide to their web user-agent, so that's something to consider and make sure the destination of the link can handle.
Putting links on a line by themselves works well too.
If you don't know what a user prefers, it makes sense to send a text/plain with links as I've described, as well as a text/html with links in tags, because tagged links may be friendlier to some users and some mail user-agents are tragically bad at their job.
[1] https://www.w3.org/Addressing/URL/5.1_Wrappers.html