Does string can get an int variable?

Your question and your code gave me different ideas about what you probably want :(
A) If you want to "print" to a string instead of the standard output, use sprintf (see: http://www.rohitab.com/discuss/topic/11505-sprintf-tutorial-in-c/[^]).
B) In your case dest array can be only used to store the count, but I would use int * instead of char *. But you can not print it directly. You will need a loop print the counts as numbers from within that loop.

But we don't do homework, we don't have the specification of it - thus go on, and try to figure out, what you missed.

[Update]
Ok, so it is an RLE, even not the finest one. But see this solution, with some comment. If C, make it C.

#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#define N 100

char *doArchive(char *str, char *dest)
{
    char tmp[10]; // needed to store intermediate results, actually should be log10(N)+2
    int idx_from;

    if(!str || !dest || !str[0]) return NULL; // check input

    *dest = 0; //make an empty result
    idx_from = 0; // start at the beginning
    do
    {
        int idx_to = idx_from + 1; // look ahead
        while(str[idx_to] && str[idx_from] == str[idx_to]) idx_to++; // find the next that does not match, or teh end of the string

        sprintf(tmp, "%c%d", str[idx_from], idx_to-idx_from); // duild the sequence code
        strcat(dest, tmp); // add it to the result

        idx_from = idx_to; // go to the next sequence
    }
    while(str[idx_from]); // until we reach the end of the string

    return dest;
}

void main()
{
    char str[N]; //the input string
    char dest[N*2]; //the longest if every character is once
    printf("Enter your string: ");
    gets(str);

    printf("Result: %s", doArchive(str,dest));
}