Wiring a outlet from an existing switch?

I have just framed a wall, now I want to install a outlet. I have a light switch about 8 feet away that is used for light, it also has 4 outlets in the master bedroom. Of the bedroom outlet only 3 plugs are being used for an alarm clock, TV, and a cable box. Can I run power off this switch, and not having the power gong off with the switch.