String reverse algorithm

I went for a java technical interview recently and they told me to write simple java method to get the reverse of a given string object. I used java's 'StringBuilder' class and it provides 'reverse()' method. I guess, I am correct. They smiled and went one step ahead. They told me to do the same thing without using any java providing function and write my own function to reverse the string. I wrote that as well. Finally they told me to write it using the recursive algorithm. I was little stuck and they moved to next question. 

I came home and though for a algorithm to reverse the string. I came up with this solution. 

We can get the character array from the given string and characters can be swapped in the following manner.

public String reverseStr(String s) {
    char arr[] = reverseStr(0, s.toCharArray());
    return new String(arr);
}
private char[] reverseStr(int charIndex, char[] arr) {

    if (charIndex > arr.length - (charIndex+1)) {
      return arr;
    }
    char temp = arr[charIndex];
    arr[charIndex] = arr[arr.length - (charIndex+1)];
    arr[arr.length - (charIndex+1)] = temp;
  
    charIndex++;
  
    return reverseStr(charIndex, arr);
}

My implementation may not be the best way of doing this. I just wanted to find an algorithm for this.