Yes, a person can get charged with a DUI in such a scenario, if the police feel that they could circumstantially prove that the person was driving earlier, while under the influence of alcohol or drugs or a combination of the two. Such cases are often hard to prove and therefore defensible, however, if the person has good legal representation. There may be many issues relating to circumstantial evidence, arrest in the officer's presence, search and seizure, etc.
While I agree with the first answer given, it is extremely unusuall that the police would even make such an arrest. It appears that you may have left a few facts out of your question. Did they follow you into the house after a chase? Did they observe you driving immediately before arresting you? These are questions that are going to arise in your case.
If you were simply sitting in your house all day and night and the police came and arrested you for no apparent reason, then the answer would be no, they should never do that. However, something inside me says that wasn't necessarily the case.
They have to prove driving for a DUI case - either by direct evidence (they saw you driving) or circumstantial evidence (they can put you behind the wheel through other means), but either way, they have to prove driving.
Not only that, they have to prove you were under the influence at the time of driving, instead of driving, then got drunk.
Your question is very vague. If you're been arrested in a situation like you describe, you'll need to get a criminal defense attorney in your area to discuss the facts and defenses.