Sounds like another miracle from The Other Brothers.

https://www.murphysmagic.com/product.aspx?id=61702

Description:

A fantastic coincidence effect that is great for all ages. Animals, colors and a puzzle. It's a no-sleight trick with a big surprise reveal. Check out the video and you'll see how it all comes together.

You show the faces and backs of a packet of oversized cards and state, "Think of a number between one and ten, and I'll deal exactly that number of cards on the table, face up." Any number is named (no force) and the dealing begins. You stop when that number of cards is dealt. You show the selection.

The cards are turned over and pieced together. And guess what? The design magically matches the name of the animal they selected earlier!

Coincidence or is it magic? That's the fun of Animal Tarot. It's by the Other Brothers, so you know it's clever, practical and easy to do. In fact, it's so easy to do that the spectator can even deal the cards themselves!

Includes Animal Tarot cards and online instructions.

This looks pretty good, but will await reviews

The question being, is it always a rat or any / all of the animals selected?

You dirty rat!

Looks cute.

yes! That's what I was wondering

Always Rat! (kind of)?
I bought this at the 2018 Blackpool convention.
It's an old principal used in a card trick that I think was put out by Repro Magic in London in the 80s.
Its OK, but you do need lots of space on a table, or, as I have been doing, on the floor!!

As shown and discussed on the current WPR, this seems clever and interesting.
I hadn’t paid any attention to it when it was first released but I’m considering picking it up now.
I’m always on the lookout for effects that I feel would be fun to show the grandkids.

I think a lot of people paid no attention to this based on the surprisingly few comments about it here.

It's a very clever application of an old idea, with a great climax. The cards are excellent quality, and this is the best teaching of the 'move' I've ever seen.
Just a shame the theme is animals: it makes it fine for family shows, but not so good with adults. The Other Brothers mention in the video that they played with several themes before settling on this one; maybe they'll release a more adult version.
The Wizard Product Review praised the principle to the hilt, when it is by no means new and has been used in several dealer releases. This is a very smart version though, and magically very strong.

I did get this and really like it a lot. I think I know why it has flown under the radar, it's because the name is terrible. It has very little to do with Tarot other than the cards are Tarot sized and you may choose to comment in the beginning that whatever animal they pick is indicative of their personality. But unfortunately I think having Tarot in the name caused many magicians to pass it by (including me) and the folks drawn to the word Tarot were likely turned off by this "magicky" effect. Oh well, that's how it goes. They blew it with the name. But I'm glad I got it because I happen to be a fan of magicky effects.

The effect is terrific and taught really well. The cards are super high quality and look very unusual, which I think is a plus in this case. I would respectfully disagree with Bob Gill in that I think the animal theme is perfectly fine for adults. Personally, I like the theme. I love how when you reveal the backs you cannot see the image right away, reminds me of one of those 3D pictures so popular 20 years ago.

The only thing I wish is that the box the cards came in was made to look like like a regular box that you may have bought in a toy store or at Target or something, and it could easily be in the same style as the back design of the cards. So I will have to spend some time making my own box. But other than that and I guess the fact that you can't repeat it, there is very little not to love about this effect and the job VI did in producing it. HIghly recommended!

So you can't make any other animal just the rat?

This trick sounds a lot like Conjurer Choice by Wayne Dobson. In that effect you have postcards the spectator seems to have a free choice but in the end he lands on the Houdini poster. Then you turn the cards over and it’s the Houdini Poster. It’s very similar to this effect.

Yes, Conjurers Choice is another good one. I would call it a 1st cousin.
The effect is about the same but the method is different.

These are both fun “coffee table tricks” which you can leave out waiting for your unsuspecting prey, err, I mean guest, to pick one up or ask about it.

Vanishing UK are selling it for £8 that's £16 off normal price

Vanishing US has it for $10 USD normally $25

Here is my humble magic review https://youtu.be/zwMsMNZ6R7A

Yes got it on sale, it’s great! And super easy

Yes, Animal Tarot and Conjurers Choice are both favs of mine and both have mostly flown under the radar.
I guess because they don't really fit into a workers set but are great for hobbyists or to leave out for guests to inquire about them.

That is exactly what I intend to do among several other magical items that are coffee "props"

It just occurred to me that for a limited time only, you can work in the fact that 2020 happens to be the Year of the Rat. Offer expires on December 31, 2020.

No. Feb. 11th 2021.