C programming: lines of text file to integer array

There are many issues.

This is a corrected version of your program, all comments are mine. Minimal error checking is done for brevity. intarr = malloc(sizeof(int) * 16); will be a problem if there are more than 16 numbers in the file, this should be handled somehow, for example by growing intarr with realloc, similar to what you're doing in readFile.

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <assert.h>

char *readFile() {
  FILE *fp;

  fp = fopen("input.txt", "r");
  if (fp == NULL)
  {
    printf("File is NULL!n");
    return NULL;      // abort if file could not be opened
  }

#define MAXLINELENGTH 255      // define a constant rather than hardcoding "255" at several places

  char* STRING;
  char oneLine[MAXLINELENGTH];
  STRING = malloc(MAXLINELENGTH);
  int count = MAXLINELENGTH;   // count mus be initialized and better declare it here
  assert(STRING != NULL);
  STRING[0] = 0;          // memory pointed by STRING must be initialized

  while (fgets(oneLine, MAXLINELENGTH, fp) != NULL)   // correct usage of fgets
  {
    count += strlen(oneLine);
    STRING = realloc(STRING, count + 1);
    strcat(STRING, oneLine);
  }

  fclose(fp);
  return STRING;
}


int *convert(char *STRING, int *nbofvalues) {   // nbofvalues for returning the number of values
  int *intarr;
  intarr = malloc(sizeof(int) * 16);
  int a = 0;
  char *ptr = strtok(STRING, " \n");   // strings may be separated by '\n', or ' '

  *nbofvalues = 0;

  while (ptr != NULL) {
    intarr[a] = atoi(ptr);

    printf("number = %s\tindex = %d\n", ptr, a);
    a++;
    ptr = strtok(NULL, " \n");  // strings are separated by '\n' or ' '
   }                            // read the fgets documentation which
                                // terminates read strings by \n

  *nbofvalues = a;    // return number of values 
  return intarr;
}


int main(int args, char* argv[]) {
  int *val;

  char *STRING = readFile();

  if (STRING == NULL)
  {
    printf("readFile() problem\n");   // abort if file could not be read
    return 1;
  }

  int nbvalues;
  val = convert(STRING, &nbvalues);  // nbvalues contains the number of values

  // print numbers
  for (int i = 0; i < nbvalues; i++)
  {
    printf("%d: %d\n", i, val[i]);
  }

  free(val);    // free memory
  free(STRING); // free memory
  return 0;
}

I'm not sure what your requirement is, but this can be simplified a lot because there is no need to read the file into memory and then convert the strings into number. You could convert the numbers on the fly as you read them. And as already mentioned in a comment, calling realloc for each line is inefficient. There is room for more improvements.