By default photoshop doesn’t have an option to save in .ico format. You need a plugin to make it work. You can find an appropriate plugin from photoshop plugin.
Download the plugin that is suitable to your operating system.
After downloading extract the zip files. Copy the ICOFormat64 file and paste it into the photoshop plugin folder.
C:Program FilesAdobeAdobe Photoshop CS6 (64 Bit)Plug-ins
Note that if you have 64bit operating system you should not go to C:Program Files (x86)
4) Now choose the “ICO (window Icon)(*.ICO)” option from Format option and choose the directory to save
5) Click on save.
You have created the .ico format icon with photoshop