You can do this manually if you know what the color is supposed to be. It is similar to the process of calibrating to a neutral sample. The results will not be as accurate as if you use a grayscale, especially with mixed color lighting.

You should work from a RAW file if available.

1. First, set a best guess white balance.
2. Measure the known color in your image in terms of R,G, and B (Red, Green, Blue) values
3. Compare the measurement to your target
4. Adjust the white balance accordingly
5. Repeat from step 2 until the color is matched

Example: if the sample is 55,87,123 and it is supposed to be 55,82,125 you will leave the red alone, take out some green, and add a little blue.

Hint (added after your followup) to make RGB edits with temp/tint:

• To add red: Add yellow and magenta.
• To remove red, remove yellow and magenta.
• To change blue, use temp.
• To change green use tint.

Caution: when sampling the color, especially a fabric use a large sample (example 20x20 pixels) instead of a point sample to get an average reading.

Be aware that there are color shifts that can occur at certain hues and values, for various reasons, that will affect some parts of the image but not others.

Another tip: If you want to save money, get some paint sample cards from a home improvement store, including neutrals, and paste them to a piece of foam board. This would be better than calibrating to a shirt.