Do I have to be an artist or have a good handwriting to start Calligraphy?
No, you do not have to be an artist or have a good handwriting to start learning calligraphy.
Calligraphy being an art of creating beautiful alphabets by giving them thick and thin strokes is finessed by a certain method and thus anyone who adheres to the methodology can master it. It is just an art of practice whereby you manipulate each or many alphabets together to create a beautiful composition. By having a command over this art you can in turn improve your handwriting.
But yes if you are an artist you can create your own unique style rather than following the general rules to learn calligraphy because artistic mind is creative