Is it possible to create an array whose length is decided by only user

You can't define an array's size using a variable. x is a variable, so a[x] isn't allowed. You have to use malloc to allocate the array's memory. Your code shouldn't even compile!

I write C++, which allocates memory differently. But I believe this is what you want:

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

int main()
{
   int x;
   printf("Enter the length of the character array:");
   scanf("%d",x);

   int* a = (int*) malloc(x * sizeof(int));
   return 0;
}

malloc allocates bytes, so you need to allocate enough of them to hold x ints. malloc returns a pointer to the memory that it allocated. That's a void*, so you have to cast it to the type you want (an int*). You can then use a just like an array: a[0]...a[x-1].