Sure. The code to use for that is something like this:
this.getField("Today").value = new Date();
Then you just set the field's Format option to Date and select the pattern you want.
This code can be included as a doc-level script, which will execute each time the file is opened, and can also be attached to a button and executed manually.
.
Visit my custom-made PDF scripts website: http://try67.blogspot.com
Contact me personally: try6767@gmail.com