I have a Slack group with a bunch of friends and we always share Spotify links. I wanted these links to be added to a big Spotify playlist automatically, so here's the solution I came up with using Zapier to bridge the gap. As I wanted to use just the free tier it required 2 separate Zaps to achieve this. Many of the solutions online offer ways to sync Spotify to Slack, but this offers the opposite.
Zapier is fully capable of handling this particular task in one Zap, the trick is that it exceeds the three action limit of the free tier, so I had to break it into two Zaps, one to handle filtering Spotify links from the #music Slack channel, and the second to parse the URL and extract the Spotify ID of the track and post it to the playlist.
Filter Spotify Links to Slack Channel
Create a new Slack channel called #spotify-links. I added a description to mine to tell people the purpose of it and to not join this particular channel. This also needs to be public, as Zapier can't see private channels.
In Zapier create a new Zap integration with Slack.
Add a filter action
Add another action and select Slack
Slack to Spotify Playlist
Create a new Zap integration with Slack -> Continue
Add a Formatter action -> Continue
Pattern -> [^\/][\w]+(?=\?)
-> Continue
And that should have you rolling. Be sure to test your data and make sure things are pulling properly along the way.