I think Szulat is not wrong when giving an suggestion to use a sphere. That is a perfectly valid suggestion. If you examine the example posted by user7677025, there is also a reflection of the lens, and it reveals the shot is indeed made by using a sphere reflection.
The only problem is that you then need something like a clean glass or plastic tube where the sphere is attached to the other end of it. Otherwise you also get the reflection of the stick or hand or what ever you use to hold the sphere on front of the scene.
But to get a good sphere reflection, it is probably better to shoot it further away, and then crop the image. Otherwise the reflection of the camera itself will look way too big in the image because usually smart phone cameras comes with a wide angle lens. Then to get a good cropped image requires a smart phone with lots of megapixels to get at least adequate results.
Another option is to use the smart phone camera's "stitch panorama feature", if there is one available. On many new smart phones there are pretty good software that does rather good quality panorama by stitching multiple shots into one. Then shoot a 360 panorama, or as "long" panorama as possible. Or use just any good landscape shot.
Next on PhotoShop (or GIMP) you can create so called "tiny planet" image by following e.g. this tutorial: Photoshop Cs5 Tutorial: The Tiny Planet Photo Effect by Justin Odisho
I will not go onto all shooting and editing details here, unless someone asks me to do so. But for example I do recommend trying to use a tripod, and attach the mobile phone onto it with a clamp if it is a stitched panorama you are shooting. And try to shoot something where's no much stuff and details on the foreground.
See also the links to similar topics on the right margin, for example to find out more about "little planet" post processing.