How hard is it to get paid to do PhD in the US as an international student in engineering?
In engineering, the primary source of support for international PhD students in the US is:


10.4% via teaching assistantships
71.7% via research assistantships or traineeships
11.5% via fellowships or grants
Small portion via other sources (e.g. self funded, employer funded).


Source: Survey of Earned Doctorates, TABLE 35. Doctorate recipients' primary source of financial support, by broad field of study, sex, citizenship status, ethnicity, and race: 2014

In STEM fields in the US, both US citizen and international PhD students are generally offered admission with funding, which will be provided via teaching assistantships, research assistantships, or some combination of the above. US STEM PhD offers that don't come with funding are generally not worth accepting. So it's not about specifically trying to get funding, it's about getting a real offer of admissions (which should come with funding).