Sublime Text doesn't provide an AppleScript suite, but does provide a command line utility ‘subl’ in:
Usage is available with
subl is aware of the current window when opening files and adds the file as a tab.
/Applications/Sublime\ Text.app/Contents/SharedSupport/bin/subl /path/to/file
To run this in AppleScript, use ‘do shell script’.
do shell script ¬
"/Applications/Sublime\\ Text.app/Contents/SharedSupport/bin/subl /path/to/file"
do shell script
"/Applications/Sublime\\ Text.app/Contents/SharedSupport/bin/subl " ¬
& quoted form of POSIX path of (alias "path:to:file")