How can I load the contents of a text file into a batch file variable?

If your set command supports the /p switch, then you can pipe input that way.

set /p VAR1=<test.txt
set /? |find "/P"

The /P switch allows you to set the value of a variable to a line of
input entered by the user. Displays the specified promptString before
reading the line of input. The promptString can be empty.

This has the added benefit of working for un-registered file types (which the accepted answer does not).