You have not inducated your basic qualification and the stream with which you opted for engineering. Now let me substantiate some facts so that you can take up Ph.D from IIT and in order to achieve the same, you may do the following points-
1) You must look out for the paper- advertisement where there is mention vacancies of the Lecturership required in IIT and there you would notice the eligibility condition for the Lecturership required in IIT. Such advertisements may appear on line as well. Assuming that you are having a high second class post graduate degree in any stream - either in pure science or in engineering stream- Chemical, Mechanical, Civil, Metallurgical etc, you can apply for the post of Lecturership in IIT. NET is the essential test to be cleared for the permanent absorption as a Lecturership.
2) With your exposure in the teaching profession in IIT, you may apply for Ph.D and finally you would be selected depending upon your merit - score in the interview and the mask earned in the qualifying examination.
While engaged in teaching profession, you would remain under surveillance where your performance would be evaluated before the selection of Ph.D.
Yes, it would be a good option for you to undertake Ph.D from IIT.
The other option would be to try in Some Regional Engineering Colleges for the persuasion of your Ph.D course.