A couple of points.

1. You need to move bits of code into functions.
> "Write two functions int is_square(int num) and int reverse(int num)"

2. Indentation matters - yes, really!
Code:
#include<stdio.h>
int main()
{
  int a, b, sum, rev = 0, remainder, i;
  printf("Please enter the two integers:");
  scanf("%d%d", &a, &b);

  sum = a + b;
  while (sum != 0) {
    remainder = sum % 10;
    rev = rev * 10 + remainder;
    sum /= 10;
  }

  for (i = 0; i <= sum; i++) {
    if (sum == i * i) {
      printf("Alice wins");
    } else if (rev == i * i) {
      printf("Bob wins");
    }
    return 0;
  }
}
So for example
- you mess up the sum value, trying to compute the rev value.
- your return 0; is inside the for loop, so your loop runs only once anyway.
- Alice always wins, because you managed to make sum = 0 trying to compute rev.