Can an immigration get residency having a DWI?

Possibly. Assuming the immigrant was convicted of a single simple DUI (no other charges and/or damage to persons or property), the immigrant will likely be able to become a permanent residence. However, DUI is taken very seriously. A conviction for any criminal offense is an adverse factor. You may be required to submit additional evidence of favorable factors. You can read more about adjustment of status at http://myattorneyusa.com/adjustment-of-immigration-status.