Absolutely yes. According to the rules of BITSAT exam as mentioned in their brochure a candidate can give the exam twice once in the same year immediately after board exams and second in the next year.

So if you are eligible for all other required minimum criteria as mentioned in the link below then you can give bitsat exam twice.

https://www.careers360.com/exams/bitsat

Hii,Yes u can give bitsat in 2020 also.Preparation Tips: BITSAT is a university level exam conducted in online (computer-based) mode. The exam offers admission into Integrated first-year programs like B.E., B.Tech and B. Pharm offered at BITS Campuses.The exam will be conducted in online (computer-based) mode. Check BITSAT Exam PatternThe syllabus will cover questions from Physics, Chemistry and Mathematics/Biology based on NCERT Class 11 and 12 of Science stream.BITSAT 2019 will be scheduled for multiple dates from May 16 to 26, 2019.All campuses of BITS (Pilani, Goa and Hyderabad) will release their individual branch-wise cut off marks after the declaration of results. Check BITSAT Cutoff.

Hope,this information will helpful for you.