It's not a problem to do your PhD studies in English, particuarly in Sciences. 

In certain areas, German ist required and helpful like in Philosphy or German Studies. It is mostly depending on the thesis’ subject and on the approval of the candidate’s supervisor. Please check the list with the offered PhD positions and see the required language skills. 

• Very good English skills if English is the language of instruction for PhD studies. No prior knowledge of German required in the following disciplines: Biology, Biomedicine, Chemistry, Pharmacy, Earth Sciences, Mathematics, Computer Science, Physics, Earth Sciences and Veterinary Medicine
  English Certificate: IELTS certificate with an overall rating of 6.5 points OR TOEFL certificate with a total score of 95 points 

• Very good German skills if German is the language of instruction for PhD studies. Usually in Humanities and Social Sciences but depending on the professors' requirements.
  German Certificat: TestDaF certificate with at least the grade 4 in all four parts and a total score of at least 16 points OR DSH-2 certificate.