Civilians can indeed get a clearance.
Its quite common with contractors...
Anybody that does job searching in the DC area will know the horrors of requiring security clearance... its quite difficult to get ajob if you can't get a clearance.
Most times the company will sponsor you to get a clearance when you come on board unless they specify "Required existing clearance".
Usually TS (Top Secret) they get a bit more strict about having an existing clearance... then you get into that whole catch-22 thing
its a real PITA to fill out all the forms (small novel) but well worth it on the resume.
Just make sure you know everytime you farted in the past 5 years

(LOTS of info required)