Yes, this is possible. You will want to look at the WebCamTexture functionality.
You create a WebCamTexture and call its Play() function which starts the camera. WebCamTexture, as any Texture, allows you to get the pixels via a GetPixels() call. This allows you to take a snapshot in when you like, and you can save this in a Texture2D. A call to EncodeToPNG() and subsequent write to file should get you there.
Do note that the code below is a quick write-up based on the documentation. I have not tested it. You might have to select a correct device if there are more than one available.
using UnityEngine;
using System.Collections;
using System.IO;
public class WebCamPhotoCamera : MonoBehaviour
{
WebCamTexture webCamTexture;
void Start()
{
webCamTexture = new WebCamTexture();
GetComponent<Renderer>().material.mainTexture = webCamTexture; //Add Mesh Renderer to the GameObject to which this script is attached to
webCamTexture.Play();
}
IEnumerator TakePhoto() // Start this Coroutine on some button click
{
// NOTE - you almost certainly have to do this here:
yield return new WaitForEndOfFrame();
// it's a rare case where the Unity doco is pretty clear,
// http://docs.unity3d.com/ScriptReference/WaitForEndOfFrame.html
// be sure to scroll down to the SECOND long example on that doco page
Texture2D photo = new Texture2D(webCamTexture.width, webCamTexture.height);
photo.SetPixels(webCamTexture.GetPixels());
photo.Apply();
//Encode to a PNG
byte[] bytes = photo.EncodeToPNG();
//Write out the PNG. Of course you have to substitute your_path for something sensible
File.WriteAllBytes(your_path + "photo.png", bytes);
}
}