Can I make a script always execute as root?

Be really careful: scripts combined with setuid are dangerous!

First, please have a look on this question/answers, especially on this answer and security warning.

If you still want to execute your script with setuid set, then you can write a short C program as wrapper and set the setuid bit on the compiled binary.

Wrapper example:

int main(void) {        
    setuid(0);
    clearenv();
    system("/absolute/path/to/your/script.sh");
}

Another solution using sudo (mentioned here):

1. As root, prevent write (and maybe other) access to your script:

   chown root /absolute/path/to/your/script.sh
   chmod 700 /absolute/path/to/your/script.sh
   

2. Verify that noone except root can replace the script, e.g. by modifying the access rights of the parent folder:

   chown root /absolute/path/to/your/
   chmod 755 /absolute/path/to/your/
   

3. Modify sudo access rights in /etc/sudoers with visudo:

   ALL    ALL = (root) NOPASSWD: /absolute/path/to/your/script.sh
   

   More details about the settings (e.g. restricting access to specific users or groups) can be found in the sudoers manpage.

Afterwards, all users can run the script as root without password:

sudo /absolute/path/to/your/script.sh

This is similar to using the wrapper/setuid solution above.

Easiest and safest way is to use SETUID bits in file permissions. that way command permissions will be elevated to file owner permissions.

to prevent script from edition do not set write for everyone bits.