If you will share the archive with other Origin users I suggest you use Origin's Opack object...
using Opack = LabTalk.Opack; Opack.reset(); Opack.FileName$ = "C:\List.txt"; // name of text file containing file list int err = Opack.pack(); // pack listed files
See LabTalk Language Reference > Object Reference > Alphabetical Listing > Opack for descriptions of all Opack properties and methods.
Otherwise you need a 3rd party program to zip the files and call the application with ExecuteApp in Global Functions > System.