This question is very similar to How to make a 3D globe. There is some difference, as that question dealt with building a globe from scratch, whereas this question has a predefined image. There is a little difference in that you'll need to manually trim the boundary of your image. Here's how did it:

pic = Import["https://i.sstatic.net/5JpK4.jpg"]; {width, height} = ImageDimensions[pic]; w = 40; h = 45; pic = ImageTake[pic, {h, height - h}, {w, width - w}]; ParametricPlot3D[{Cos[u] Sin[v], Sin[u] Sin[v], Cos[v]} , {u, 0, 2 Pi}, {v, 0, Pi}, Mesh -> None, PlotPoints -> 100, TextureCoordinateFunction -> ({#4, 1 - #5} &), Boxed -> False, PlotStyle -> Texture[Show[pic, ImageSize -> 1000]], Lighting -> "Neutral", Axes -> False, RotationAction -> "Clip", ViewPoint -> {-2.026774, 2.07922, 1.73753418}, ImageSize -> 600] 

This question is very similar to How to make a 3D globe. There is some difference, as that question dealt with building a globe from scratch, whereas this question has a predefined image. There is a little difference in that you'll need to manually trim the boundary of your image. Here's how did it:

pic = Import["https://i.sstatic.net/5JpK4.jpg"]; {width, height} = ImageDimensions[pic]; w = 40; h = 45; pic = ImageTake[pic, {h, height - h}, {w, width - w}]; ParametricPlot3D[{Cos[u] Sin[v], Sin[u] Sin[v], Cos[v]} , {u, 0, 2 Pi}, {v, 0, Pi}, Mesh -> None, PlotPoints -> 100, TextureCoordinateFunction -> ({#4, 1 - #5} &), Boxed -> False, PlotStyle -> Texture[Show[pic, ImageSize -> 1000]], Lighting -> "Neutral", Axes -> False, RotationAction -> "Clip", ViewPoint -> {-2.026774, 2.07922, 1.73753418}, ImageSize -> 600]