On *nix, you can use chmod +x file.sh to make a .sh file executable.
Terminal
$ ls -lsah
total 12K
4.0K drwxr-xr-x 2 mkyong mkyong 4.0K Feb 5 10:24 .
4.0K drwxr-xr-x 17 mkyong mkyong 4.0K Feb 5 10:24 ..
4.0K -rw-r--r-- 1 mkyong mkyong 67 Feb 5 10:24 run-script.sh
$ chmod +x run-script.sh
$ ls -lsah
total 12K
4.0K drwxr-xr-x 2 mkyong mkyong 4.0K Feb 5 10:24 .
4.0K drwxr-xr-x 17 mkyong mkyong 4.0K Feb 5 10:24 ..
4.0K -rwxr-xr-x 1 mkyong mkyong 67 Feb 5 10:24 run-script.sh
Above example, assign an execute permission +x to run-script.sh