An Eye-Fi card will do that. I've just set mine up this morning to send photos directly to my Android phone without the need for a hotspot/router etc.. You run Eye-Fi software on the Android, which is a free download, and that acts as a server to receive the image files and display them on the phone(tablet) as they are received.
In order to avoid the need for a hotspot/router you configure the Eye-Fi card to run in Direct Mode. The card itself then becomes its own Hotspot (without connection to the internet) and you set your phone/tablet to log on to the WiFi network provided by the Eye-Fi card.
Of course you can also connect the devices via a common Hotspot, like a home router, and that works too.
I would say that setting this up is far from intuitive, and as I hate to read instructions I did bumble my way towards the solution.
There are examples on Youtube to show these things in action.