How an international student can get a grant by himself?
Typically grants for international students in the U.S. are extremely limited because all government/state grants are only for US citizens or permanent residents (you need to have a green card). Depending on your field though private companies, NGOs and other entities whose funding doesn't come from public sources, will have grants that are open to non-US citizens. 
The other option is to apply to grants through your advisor, so he would "sign" the grant proposal under his name but you prepare the proposal. Keep in mind that in this case if anything happens with your advisor he/she is holder of the grant and can decide how to spend the money. For example he might pick another graduate student. Although I imagine in Engineering big private companies might have incentives to pay a PhD student to work on something that will profit them as well.

It is extremely rare for non US citizens to find grants that will support the full duration of the PhD. Another option is Fullbright. Your best option though is to find an advisor who can guarantee at least 1-2 years of salary/tuition to get you started, otherwise you might have to TA to pay for your salary.