One of Matrix's most ambitious goals is to bridge its network to as many others as possible. It's an awesome goal, and we're hosting a Discord to Matrix bridge on exozyme. Note that only exozy.me accounts can use the bridge. If you want to bridge your Discord guild (server), use the t2bot.io bridge instead since it's more robust.
Start a chat with the bridge bot, and type
help to see instructions. Now retrieve your Discord account token using this method or this one. All you need to do now is type
link user YOURTOKEN to the bot and enjoy the bridge! Note that linking your account token is against Discord's Terms of Service and may get your account disabled.