See: Qualifications. It is EXTREMELY DIFFICULT to become an FBI Special Agent. Like, harder than getting into Harvard difficult. It’s hard enough to be hired as FBI Professional Staff—the Janitors have to go through the same process as the Intelligence Analysts. But you want to be a Special Agent? Good luck.
Assuming you have the physical, mental, emotional, and age qualifications we’ve listed and are dead set on becoming a Special Agent, the odds are still tough. The FBI employs roughly 36,000 people, but less than a third of those employees—around 14,000—are Special Agents. 14,000 may sound like a big number, but consider that over 21,000 people applied to become agents in 2010, and Special Agents hold their positions for several decades. To further put that number in perspective, the Los Angeles Police Department, the third largest in the U.S., consists of about 10,000 uniformed officers. The Chicago Police Department has about 12,000. The New York Police Department, the largest in the country, employs about 35,000 uniformed officers (as much as the entire FBI, Special Agents and Professional Staff), as well as several thousand Auxiliary Officers, School Safety Agents, and Traffic Cops. That’s for an area of under 500 square miles; the FBI is responsible for enforcing federal law throughout the entire country—close to 4,000,000 square miles, but you knew that—as well as within many U.S. embassies overseas. So yeah, it’s a bit competitive.