If a police officer comes to your home and asks to come inside, you have the right to say no. With a few exceptions, a lack of consent typically means that the officer has to go and get a warrant. Only then can they enter your home without consent.
That said, as an immigrant, you may be more worried about a visit from ICE (Immigration and Customs Enforcement) agents. They handle immigration issues and often work to deport those who they do not believe should be in the United States. If they come to your home, can you deny them entry? Do they need to get a warrant to enter, just like a police officer?
Warrants are needed to enter homes
ICE tends to use both search warrants and arrest warrants. They need to have one or the other to enter your home. Judges can hand out search warrants, just as they do for the police, while arrest warrants can come from ICE itself.
That said, ICE has been very clear that they can make arrests without warrants. They just have to do it in a public space. Again, they compare this to the role of police officers, who can make arrests in public areas when they have a valid reason to do so. The warrant doesn’t always have to be given out in advance.
Your home, however, is not a public space. You have a right to safety and privacy, and so agents do need to get a warrant first before coming into your home. If they fail to do this properly, you need to know exactly what options you have.