Hello, yes you can do a bachelor in engineering in the US. Your Bachelor in arts degree won't affect your admission process as you will be accepted on the basis of your 11th and 12th marks, SAT and IELTS score. These two tests are conducted yearly and you can easily apply for them online. SAT will test your qualitative, quantitative, logical reasoning, verbal and non verbal skills. IELTS will test your English proficiency.

You need to have a minimum 3.0 GPA in your 12th ,along with that you need to have some extra curricular activities and letter of recommendations from your teachers/if you have interned at a firm or organization as well which will make you stand out from the rest. Some colleges in America also need you to submit an essay along with your admission application and transcripts as to why you want to pursue a course in XYZ college so make sure you check it up online accordingly.

All the best!