Yes! The right to organize a union in the private sector is protected by federal law. States can't take your right to form a union away and employers can't make you sign it away.
Things get a bit more complicated if you work in the public sector. It depends on the department or agency you work within and can vary widely so be sure to check the relevant statutes in your state or municipality. For example, here is a map of where public school teachers can collectively bargain.
Also, 27 states have passed right-to-work laws. These laws, however, don’t prevent you from unionizing. They may make it harder for unions to collect dues, but that doesn’t make unions illegal there and shouldn’t stop you from forming or joining one. Labor organizations operate in all U.S. regions supporting workers through negotiations for better conditions on the job. And while union membership has been on the decline over the past few decades, a new fervor for unions has sparked increased organizing activity.
Are you in a state with low union density and aren’t sure where to start?
Workers are building power across the country. Look for local resources like existing unions in your state. Then look for examples of unions that organize within your industry in other parts of the country.