To get invited to ani-cli matrix space please knock into the #ani-cli-queue:matrix.org room.
In the reason field, please mention that you want to be invited to ani-cli. If your main client does not support spaces, please add that to the reason.
Knocking is not supported by every client yet. You can use nheko. In nheko, click on a plus icon in the down left corner, join room, input #ani-cli-queue:matrix.org into the "Room ID or alias" input box. It will say that you are not allowed to join and ask if you want to knock.
It might take some time before you get invited.