Hey! So, I'm not an engineer, but my situation is quite similar. I'm in a somewhat related field and my profile is almost identical to yours: international student, liberal arts college in the US, good GPA, research experience but no publications, etc. I've gotten into some excellent PhD programs for my field so far: Stanford, Cornell, Universty of Rochester---and all with funding! So, unless you're dead set on like...MIT or something, I think you definitely have a good shot, even without a Master's (those usually aren't funded).
As for things you can do, definitely maintain (or improve) your high GPA, make good use of the summer, and start thinking your LoRs:
During the summer, try your best to either get a good internship (preferably in a research role), or more research experience. If your past research has been at your home institution, it might be worth looking for an external research program (REUs are rare for international students, but not nonexistent). Otherwise, see if you can continue research with your previous advisor, and see if you can push it to the point where you can present a poster at a conference or start preparing a paper. Even if these things haven't happened by the time you apply, as long you've started working towards it, your advisor should be able to talk about it in your LoR for a boost.
Decide on who you want to write your LoRs as soon as possible. If you enrolled in a class with them, let them know about your plans for grad school and that you might ask them for a letter. If there are people you haven't talked to in a while, shoot them an email or find them, and give them an update on your plans. It's also a bonus if your letter writers know you personally, in addition to your academic records, as that will help them write less "standard" LoRs.
Finally, start thinking about what kind of research you'd like to do during your PhD. Being specific about the research areas you're interested in will help you with school selection, and help your letter writers tailor their letters better. It will also help you when you demonstrate familiarity and (at least some) knowledge about your proposed research areas later on in the process when you write your SOP.
Best of luck!