Dear student,
Yes, sun is a star, the following points can be considered while we say sun is a star:-
1) The Sun is one out of billions of stars. The Sun is the star at the centre of the Solar System.
2) A star mostly gives off light and heat, As sun is a star it also gives off light and heat.
3) The Sun is the closest star to Earth,So it appears larger in size.
Regards.