Rotate right and left program without operators? (<<, >>)

If you mean you are reading the characters direct from the user, so you are dealing with a char array, then no, you can't use the shift operators to rotate anything.
You have options:
1) Convert the user input to a number, and rotate that using the shift operators.
2) Manually rotate the bytes.

The first is trivial and you should be able to cope with that pretty easily.
The second is also simple, when you think about it. But ... this sounds like homework, so no code!
To rotate an array of characters right, start at the right hand end.

Remove the last digit and save it in a temporary register.

Loop through the remaining bytes copying each into the array index one greater.

When you have moved them all, put the character you saved in the first position.

Rotating left is much the same operation, but with the directions reversed.

printf("\nEnter 8 bit binary number to perform shift and rotate operations:  ");
	scanf_s("%d",&bin3);
	b=bin3;
	//read binary number to an array
	//from lsb to msb
	while(m<8)
	{
		shift_array[m]=bin3%10;
		bin3=bin3/10;
		m=m+1;
	}
	printf("\nHow many times you want to shift/rotate ");
	scanf_s("%d",&j);
	n=j;

	//circular shift right

	printf("\n\nCircular Shift/rotation (Right)\n");

	while(j>0)
	{
		printf("%d",shift_array[j-1]);

		j=j-1;;
	}
	bin3=b/pow(10.0,n);
	if(bin3!=0){
		printf("%d ",bin3);
	}

	//circular shift left
	j=n;
	printf("\n\nCircular Shift/rotation (	Left)\n");
	while(j<8)
	{
		printf("%d",shift_array[7-j]);

		j=j+1;
	}
	j=n;
	while(j>0)
	{
		printf("%d",shift_array[7-k]);
		k=k+1;
		j=j-1;;
	}