You can think of the requirement by first thinking of the function of the rebar, which is to add strength, but not just any kind of strength: specific kinds of strength. The function, therefore the requirement, is to reinforce the concrete such that it stands up to all forces it is exposed to. The concrete itself is extremely hard. That gives it a certain kind of strength. For example, it's extremely hard to compress concrete. However, concrete doesn't have as much tensile strength or shear strength. These are the kinds of loads that rebar reinforcement is designed to handle. The size and context of column footers vary so dramatically -- from a pier block for a shed to a fifty-ton point load for a parking garage -- no single standard can be assigned to all footers.
Rebar comes in a variety of sizes, approximately one half-inch in diameter. The surface is textured so that once it is cast in concrete, it will not spin or pull out. Rebar is even available in a variety of materials such as stainless steel, though mild steel is by far the most common. When rebar is called for by an engineer, architect or general contractor, the specification will often indicate that the rebar should be built to code. Generally, if an engineer officially approves specifications that diverge from local codes, they will be acceptable. Engineered specs are more likely to be even stronger than code, and plans must still be approved in advance.
Every place in the United States is subject to the jurisdiction of a set of building codes. As a rule of thumb, you should check with the smallest and nearest municipality first, going from city to county to state, for example, to determine requirements in your area. The trend in building codes is toward national and international standards, which many municipalities are adopting. Often, the national code or international code will provide a good approximation of what is required, but you should never take a risk. Get a building permit. Get your plans approved. And get your project inspected along the way to make sure. The alternative to following local rules may result in your job getting shut down.
While referencing guidelines in an international code in your planning stage isn't a bad idea, always locate the jurisdiction governing building in your area well before any building starts. Get a building permit. Get your plans approved. And get your project inspected along the way to make sure. If you have any questions, ask them in advance. The alternative to following local rules may result in your job getting shut down.