Can international students in USA intern in summer in industry?

Yes you can, and this is exactly what CPT is for. (assuming you get paid for the internship. If you are not being paid - I'm not sure what the rules are, but it might be easier than CPT)

You can do it for up to 12 month (not necessarily consecutive) during your degree. Check again with your international Office for the exact rules (you might still need to be enrolled to 12 units if not summer quarter/semester).

I was an international undergraduate in the US and I participated in summer research programs twice during those 4 years. This is slightly different from what the OP is asking, since I was working at a different university as opposed to a company. The way it worked for me was the following: I needed a faculty member at my home institution to be my 'sponsor', and I had to register for a 2 credit course over the relevant summer. Having finished my summer research, I was required to give a presentation (to some sort of relevant audience, for example, once to an 'Introduction to Research' class) and submit a journal/report. I believe my supervisor from the institution where I did my summer work was asked for a short report on my activities. That was all.

The biggest hurdle for me was to find summer programs which are willing to accept international students, or at least to fund us (in mathematics, for example, REUs are typically funded by the NSF, which prevents them from accepting international students). In Math I was only able to find 2-3 programs which would do so. There were many more in biology/biochemistry. I have a list around here somewhere if anyone is seeking such information. On the other hand, this might be different if one is looking at industry.