Yes, but it depends on the job. A gray card is mainly useful as a neutral reference for exposure and white balance. For white balance only, a plain white sheet of paper lit by the same light as your subject can work, and some photographers also use a thin white paper over the lens to create a custom WB reference.

For exposure, substitutes are less reliable unless you know how to compensate. A white card can be used if you increase exposure appropriately compared with a gray reference. Another practical metering substitute is the palm of your hand or a Caucasian face in the same light; these tend to meter about 1 stop brighter than mid-gray, so you compensate accordingly.

The key requirement for color correction is neutrality: the card or paper should be truly neutral, not tinted. That means random colored paper or paint samples may not be dependable for accurate color work.

So: DIY is possible, especially for white balance, but for consistent exposure and color accuracy, a real gray card is usually the simplest and most reliable option.