I am divorced with one child. This year my ex-spouse, who is the noncustodial parent, is entitled to claim our child as a dependent. May I still qualify as head of household?

Yes, you may still qualify as head of household even if your ex-spouse, the noncustodial parent, is entitled to claim your child as a dependent.

To qualify for head of household status, you must meet the following requirements:

1. You are not married or are considered unmarried on the last day of the year.
2. You paid more than half of the cost of keeping up a home for the year.
3. Your home was the main home of your child for more than half of the year.
4. Your child is your qualifying child for purposes other than the dependency exemption and the child tax credit.

According to the retrieved information, a custodial parent may still be eligible to claim head of household filing status based on a child even if they have released the claim to exemption for the child to the noncustodial parent. The noncustodial parent can claim the child as a dependent and for the child tax credit or credit for other dependents, but cannot claim the child for the purpose of head of household status, the earned income credit, the credit for child and dependent care expenses, or the exclusion for dependent care benefits.

Therefore, as long as you meet the other requirements for head of household status, you can still file as head of household even though your ex-spouse is claiming your child as a dependent.

Sources:
§ 152. Dependent defined
Publication 501 (2023)