If you want to ignore the negative sign then you can treat all numbers as being positive so one way to do that is to make any negative number be a positive one. Here's one way you can do that :
int main ()
{
int num, sum = 0;
scanf("%d" , &num);
if( num < 0 )
num *= -1;
while(num!=0){
sum += num % 10;
num = num / 10;
}
printf("Suma cifrelor este %d",sum);
return 0;
}