If you want to do it from inside Execute Shell step, you've got to write a shell script that will read the file line by line and add them to environment variables.
Assuming your properties file is of format:
var=value
A very basic version of the script would be:
while read line; do
export $line
done <your_props_file_name
The problem is, these variables will only be retained for the duration of that "Execute Shell" build step. Once you move to a different Build step or Post-build step (within the same job), they will be gone. This is Jenkins's cleanup by design.
That's why there is that EnvInject plugin, it takes care of maintaining the environment variables between the build steps.