Lease rules
Can my landlord refuse to rent to me because I have children?
Generally no. The federal Fair Housing Act bans discrimination based on familial status, which covers families with children under 18, with narrow exceptions such as qualifying senior housing.
Landlords can enforce reasonable, evenly applied occupancy limits based on safety and space, but can't set blanket no-children rules, steer families to certain floors or buildings, or charge extra deposits only for kids.
Many states and cities protect additional categories, such as source of income or marital status. Federal law also has limited exemptions for some small owner-occupied buildings.
If you think you were turned away for having children, write down what was said and when, and keep any ads or messages. You can file a complaint with HUD or your state fair housing agency.
Do something about it
The Tenant rights by state turns this answer into action.
General educational information, not legal advice. Laws vary by state and city and change over time - for a specific situation, contact a local tenant-rights organization.