How can you invite people outside of Roblox to become friends / play with you?

Solution 1:

ROBLOX has never supported a way to externally get someone to join your game, since it's required to own an account to play games. The same is true for friends.

There is no external option for adding a friend. You must type out the name or send a link to your profile.
The only external option for joining the same game is a private server link, but as it is private, only you and your friends will be in there.

For internal options, the party feature in Roblox's chat function (usually found on the bottom right of the screen) allows you to invite players to a game you are currently playing, but they must be on your friends list or in the party.