Not at the moment. For the time being, if you would like to cycle through dimensions on any UI object in Qlik Sense, you can drag-and-drop any field name (or a master dimension item) from the left taskbar in edit mode, and drop it into any table or chart. A pop-up will then appear and ask if you would like to replace the current dimension.
To replicate this functionality you could create a island table with the cycle group values. E.g. Blue, Red, Yellow
Then in your expression code you have a conditional statement to refer to the selected value of this island and act accordingly.
I've described one way to do that at Emulating cyclic dimension group in Qlik Sense Desktop
Take a look at sample application there.
Best regards, Vadim
I have added an extension object to make this a little easier. As Damien suggests, it requires a data island of the list of dimensions you want to use. The extension is just a variation on the horizontal list box that makes it a bit nicer to display the list of options.