There is, but it’s a little more involved and it depends on how your data is set up. You can filter your list so only the first row is ever displayed. This will cause it to swipe to the same row every time. Then create a custom action so whenever you swipe, you set a column value or increment a value. This value is then used to set a single relation and a series of lookups that you can then display in your swipe card.
This isn’t an exact example, but I use a similar method in the swipe tab here. It not exactly a random swipe in my case, but maybe it will give you some ideas on how to structure things: