Is there some expression that means "голос с хрипотцой" in English?
"голос с хрипотцой" means something near "low voice" but it is not exactly what i need. I know there is a word 'raspy' that means 'хриплый' and also 'raspy sound', but don't know is it correct to say : "This man has rasp voice" or "raspy voice" or 'his voice sounds raspy'
I believe the word you are looking for is "deep", if you what you have in mind is a low, manly, rather more serious, and naturally sounding voice.
Best of luck.