<p>I am trying to 3D print an iPhone case, however, I want it to print standing up. Is this possible to do?</p>

<p>I have a picture of the case in the link below.<a href="https://i.stack.imgur.com/dUYr0.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/dUYr0.png" alt="iphone case"></a></p>

Yes this is possible. For an FDM/FFF printer, you'll need to print with supports. I might also recommend printing in PLA to minimize the chance of warping during the print (from experience).
It might also help to slow down the feedrate to ensure smooth surface finish and avoiding delamination on such small layers.
You'll probably see a decrease in the surface quality on the inside due to the printing of support scaffolding depending on the slicing engine you use.
However
You'll want to pay attention to the strength of the case. If you print the case upright then it will be more susceptible to breaking without post-processing.
Conclusion
Ultimately, if you can get away with it, it would be better to subtract the star instead of extruding it in the model. Then you can simply print the case back face down on the plate with much better results.