yes it is possible to become an engineer after doing BSc in Physics.

To discuss how it is possible I would need to consider two scenarios, the first one being that reader is Indian while the second being reader from another country.

For reader in India, your route to get an engineering degree after BSc Physics can have three variations depending on which degree or course you want.

There are these ways,

1. BSc (Physics) →MSc (Physics/Electronics) →Mtech (Mechanical/Electronics/Electrical/Physical)
2. BSc (Physics) →MCA →Mtech (computer science)
3. BSc (Physics) →Btech

The first one is the simplest and least time consuming, taking you 4 years to finish MSc and Mtech. The second one takes the same time and is only good for those who want to pursue computer engineering. The third one will take you the most time. You will be placed in 2nd year Btech course after finishing BSc and 3 years of Btech have to be covered by you. After which if you do 2 years of additional Mtech, your total shall be 5 years.

Coming to the different exams that corresponds to a particular course, there is

1. IIT-JAM (Indian Institute of Technology Joint Admission test for Masters) for MSc/MS (Physics, Geophysics, Electronics, etc), dual MSc-Mtech(Material science specializing in nanotechnology, photonics, geophysics, etc) and integrated PhD courses. Eligibility: BSc (Physics).
2. GATE (Graduate Aptitude Test for Engineering) for Mtech, MS, and integrated PhD. Eligibility: Btech/MSc/MCA.
3. LEET (Lateral Entry Entrance Test) for Btech (2nd year) . Eligibility: BSc (Physics)/Btech (1st year).
4. Also different universities have different lateral entry programmes. It's good to check websites of IITs, IIITs, NITs, State universities, National Universities and private universities for their own lateral entry scheme.

Now coming to people outside India. There is a possibility to jump to some engineering courses after having an undergraduate major in physics. Graduate courses in electrical, electronics, photonics and so on, are usually available. It's best to check different universities for their requirements.

Also for those who haven't been able to get enrolled in any graduate engineering course, you can always try getting a PhD more inclined towards engineering, since PhD programmes are always more interdisciplinary.