Yes, you can if it is available through the insurance company, and you qualify for the coverage based on your age and health.
Some insurers offer as little as $5.000 of permanent life insurance coverage, usually through guaranteed issue life insurance policies.
In addition, insurers offering term life usually offer a minimum of $50,000 of coverage; however, some like Globe Life may offer as little as $5,000 of coverage.
So, you should be able to purchase $20,000 of life insurance, although most plans start at higher limits of coverage.
Learn more about buying $20,000 of life insurance coverage.