Can I get admission in IIT Jodhpur without taking the JEE exams?

No, for every bachelor's course offered at IIT Jodhpur, you have to clear JEE Exam and get a rank that qualifies you for admission. Some IITs accept Bachelors admission with JEE Rank but not for engineering courses. For instance, IIT Madras offers a Bachelor's program in the Humanities department for which you only need to clear HSEE. 

Here are the programs offered by IIT Jodhpur and the exams accepted respectively 

However, every engineering course requires JEE rank for admission irrespective of any IIT.