Yes cats can get hiccups It may be because he is eating too fast or too much at a time. How often are you feeding him? if only twice a day then I would suggest increasing it to 3 or 4 times a day, so he doesn;t get so hungry and gulp his food. Give him the same amount per day, but divide it into more meals.
Also to make him eat more slowly, you can raise his dish slightly, e.g. put the dish on an upside down cereal bowl, if he will accept this.
If the hiccups still persist, then I would ask the vet for advice in case something is wrong, particularly if they are protracted attacks of hiccups each time.