'I'm hungry' is correct.
You could also say:
'I'm a bit hungry' - when you are hungry, but it's not urgent that you eat
'I'm a little hungry' - a more polite version
'I'm feeling a little hungry' - a more polite version
'I'm getting hungry' - if have just started to feel hungry
'I'm very hungry'
'I'm starving hungry' - you really need to eat soon!