Yes, you can. You can write, file, and prosecute a patent application for your invention all by yourself.

But as with performing your own brain surgery, rarely is it advisable to enter such difficult waters without the services of a well-trained professional.

What makes patenting so difficult?  For starters, there are the labyrinthine federal statutes, as well as the a 4 inch thick set of rules promulgated by the United States Patent and Trademark Office.  Moreover, the courts, and particularly the United States Court of Appeals for the Federal Circuit, which hears all patent appeals (and for nearly all practical purposes decides which patents have teeth and which are toothless), have changed directions repeatedly over the last several years, so much so, many patent attorneys have trouble keeping up.

If your budget leaves no other options, however, at least read and heed "Patent It Yourself" by David Pressman, which its publishers, Nolo Press, allege is the "world's bestselling patent book".  Good luck.