I was given a 10yr UK visa ban in 2015. I recently got admission to a US university for masters.
Can the existing UK ban affect my chances of getting the US visa? What other countries can I migrate to?
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Yes, it can affect your chances of obtaining a US visa.
This 2015 question is similar, and has a relevant answer that addresses your question. Since the answer was posted the law has not changed in favor of applicants.
In the answer posted October 2, 2015, a well-respected member of this community wrote:
Yes, they share information. The controlling reference for this is a treaty between the US and UK which was drafted in 2013 and entered into force last year (2014) which says in part...
CONSIDERING that the effective administration and enforcement of the immigration and nationality laws of the United States of America and the United Kingdom are important to protect the health and safety of their populations, to maintain the security of their societies, and to promote international justice and security by denying access to their territories to persons who are criminals or security risks;
ACKNOWLEDGING that identification of individuals who are inadmissible under their respective immigration laws enhances their ability to facilitate the travel of bona fide visitors;
So the answer is yes, the two governments share information, not only by this treaty (and similar ones), but also by terms implicit in the "Special Relationship".
Based upon all of this, it is natural to conclude that a pejorative history in one of the signatories will affect visa decisions in the other signatory. This does not mean visa applications will be automatically refused, the decision-maker in each country will decide based upon all available information and sometimes this can be favourable to the applicant; but most of the time it would not be favourable to the applicant.
Thus, your UK ban clearly carries a negative effect. Based on that negative effect, the US may deny your application. If your US application is otherwise exemplary, the US may grant you a visa. Whether your US visa application will be granted or denied, however, cannot be known in advance: the only way to know for sure is to apply for a US visa.