You will absolutely get strong, sculpted arms if you do CrossFit because so many of the basic exercises involve the upper body. Some use equipment and some are just bodyweight, but they all strengthen your arms. If you're not into CrossFit, that's OK! You can still benefit from working your upper body with these effective exercises, many of which you can do at home, as long as you have a pair of dumbbells or a wall. Some of these moves are good for beginners and some are more advanced, but no matter what, you can take a few of these exercises to create your own upper-body workout.
Use sliders or two hand towels on smooth surfaces, or paper plates on carpet. If you don't have enough space to walk your plank, just do plank ups with sliders. If you don't have sliders, towels, or paper plates, just do mountain climbers.
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Lunges are defintiel a lower body exercise, but holding a weight overhead turns this into an arm workout.