It isn't that hard to deal with the character array itself without converting the array to a string. Especially in the case where the length of the character array is know or can be easily found. With the character array, the length must be determined in the same scope as the array definition, e.g.:
size_t len sizeof myarray/sizeof *myarray;
For strings you, of course, have strlen available. 
With the length known, regardless of whether it is a character array or a string, you can convert the character values to a number with a short function similar to the following:
/* convert character array to integer */
int char2int (char *array, size_t n)
{    
    int number = 0;
    int mult = 1;
    n = (int)n < 0 ? -n : n;       /* quick absolute value check  */
    /* for each character in array */
    while (n--)
    {
        /* if not digit or '-', check if number > 0, break or continue */
        if ((array[n] < '0' || array[n] > '9') && array[n] != '-') {
            if (number)
                break;
            else
                continue;
        }
        if (array[n] == '-') {      /* if '-' if number, negate, break */
            if (number) {
                number = -number;
                break;
            }
        }
        else {                      /* convert digit to numeric value   */
            number += (array[n] - '0') * mult;
            mult *= 10;
        }
    }
    return number;
}
Above is simply the standard char to int conversion approach with a few additional conditionals included. To handle stray characters, in addition to the digits and '-', the only trick is making smart choices about when to start collecting digits and when to stop. 
If you start collecting digits for conversion when you encounter the first digit, then the conversion ends when you encounter the first '-' or non-digit. This makes the conversion much more convenient when interested in indexes such as (e.g. file_0127.txt).
A short example of its use:
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
int char2int (char *array, size_t n);
int main (void) {
    char myarray[4] = {'-','1','2','3'}; 
    char *string = "some-goofy-string-with-123-inside";
    char *fname = "file-0123.txt";
    size_t mlen = sizeof myarray/sizeof *myarray;
    size_t slen = strlen (string);
    size_t flen = strlen (fname);
    printf ("\n myarray[4] = {'-','1','2','3'};\n\n");
    printf ("   char2int (myarray, mlen):  %d\n\n", char2int (myarray, mlen));
    printf (" string = \"some-goofy-string-with-123-inside\";\n\n");
    printf ("   char2int (string, slen) :  %d\n\n", char2int (string, slen));
    printf (" fname = \"file-0123.txt\";\n\n");
    printf ("   char2int (fname, flen)  :  %d\n\n", char2int (fname, flen));
    return 0;
}
Note: when faced with '-' delimited file indexes (or the like), it is up to you to negate the result. (e.g. file-0123.txt compared to file_0123.txt where the first would return -123 while the second 123).
Example Output
$ ./bin/atoic_array
 myarray[4] = {'-','1','2','3'};
   char2int (myarray, mlen):  -123
 string = "some-goofy-string-with-123-inside";
   char2int (string, slen) :  -123
 fname = "file-0123.txt";
   char2int (fname, flen)  :  -123
Note: there are always corner cases, etc. that can cause problems. This isn't intended to be 100% bulletproof in all character sets, etc., but instead work an overwhelming majority of the time and provide additional conversion flexibility without the initial parsing or conversion to string required by atoi or strtol, etc.