Yes. There are numerous amateur and pro videos on the internet that demonstrate how to to do it. I would be very, very afraid to do that myself, though. I would at least ask the guy at the camera store if I could watch him do it once before I felt comfortable enough to start doing it myself.
You can get an air blower (not the kind with a chemical propellant in it, I think) and you might be able to clean your sensor well enough without having to actually touch the sensor. Just lock the mirror up and gently blow the air on it.
Scott
Canon 5d mk 4, Canon 6D, EF 70-200mm L f/2.8 IS mk2; EF 16-35 f/2.8 L mk. III; Sigma 35mm f/1.4 "Art" EF 100mm f/2.8L Macro; EF 85mm f/1.8; EF 1.4x extender mk. 3; EF 24-105 f/4 L; EF-S 17-55mm f/2.8 IS; 3x Phottix Mitros+ speedlites
Why do so many people say "FER-tographer"? Do they take "fertographs"?
