No, there is not a cookie law in the US. However, some states have laws that regulate cookie usage as it relates to their residents, like the California Consumer Privacy Act (CCPA).
Non-US cookie regulations may also apply to US websites. For example, the General Data Protection Regulation (GDPR) applies to all businesses that market to EEA consumers. US websites who have non-US visitors may need to evaluate where their users are based to understand what cookie laws they need to follow.