You have to use @BotFather, send it command: /setjoingroups There will be dialog like this:
YOU: /setjoingroups
BotFather: Choose a bot to change group membership settings.
YOU: @YourBot
BotFather: 'Enable' - bot can be added to groups. 'Disable' - block group invitations, the bot can't be added to groups. Current status is: DISABLED
YOU: Enable
BotFather: Success! The new status is: ENABLED.
After this you will see button "Add to Group" in your bot's profile.