Yes, with limitations. There are a number of work options available to F1 students.
Below we detail the general work options available to students. See this article for an analysis of work options specifically for startup founders in F1 status.
F1 students can work as long as their employment has been approved by their university in one of the following categories:
1. On-Campus Employment: An F-1 student can work on campus or at an off-campus location affiliated with the school without special authorization. This includes things like working in the school bookstore, or being hired as a research assistant through the school. Unlike CPT and OPT, on-campus employment can begin immediately--there is no one-year waiting period. You may work on-campus for 20 hours a week while classes are in session, and 40 hours a week during summer and breaks. Time spent in an on-campus job does not affect the amount of time you may later work on CPT or OPT.
2. Curricular Practical Training (CPT): CPT is work directly related to your major study area that is carried out before graduation. It may be paid or unpaid, and in most cases may start only after you have been in F-1 status for at least one academic year.
There is one exception to the one-year rule: if your course of study requires starting an internship immediately as part of your studies, the CPT may start sooner. Courses of study that allow this are often called "Day-1 CPT" programs.
Unlike on-campus employment, you must get special authorization from your school to start CPT. Although exceptions apply for programs that require full-time externship work as part of the course of study, students normally may work in CPT for a maximum of 20 hours a week while classes are in session, and 40 hours a week during summers and breaks.
Part-time CPT never affects future eligibility for OPT. Full-time CPT, on the other hand, has an all-or-nothing effect on OPT. If over the course of your studies you work for fewer than 12 months on full-time CPT, your OPT eligibility will not be affected at all. If you work for 12 months or more, however, you will not be eligible for any OPT. For instance, a student who has worked 11 months of full-time CPT and 30 months of part-time CPT remains eligible for a full 12 months of OPT upon graduation, but a student who worked for 12 months of full-time CPT during her studies is not eligible for any OPT.
3. Optional Practical Training (OPT), First Year: OPT is work directly related to your major area of study carried out during your studies or up to 14 months after graduation. Every F-1 student gets 12 months of OPT. Like CPT, OPT may only be started after you have been enrolled in F-1 status for at least one academic year. Note that while OPT may occur before or after graduation, any OPT you use before graduation will be subtracted from the total amount available to you. So, if you are applying to work before graduation, try to apply for CPT instead of OPT to preserve as much of your OPT time as possible for post-graduation work.
OPT may be paid or unpaid, and one of the biggest perks is that it allows self-employment, meaning you can start and work for your own business in the US, as long as it is related to your major field of study.
4. Optional Practical Training (OPT), STEM Extension: If your degree was in a STEM field, you may extend your OPT for an additional two years (for three years total). STEM Extension OPT has several restrictions that the first year of OPT does not, however: STEM Extension OPT does not allow self-employment. The STEM OPT graduate must be a bona fide employee of the company hiring them. The employer must register for the Department of Labor's E-Verify service, and sign off on a formal training plan explaining what the STEM employee will learn and how they will be supervised during the STEM extension. The employer must also agree that the STEM OPT employee will receive compensation "commensurate to that provided to similarly situated U.S. workers."