In top IIT's DELHI ,MUMBAI ,KANPUR , MADRAS , KHARAGPUR , RORKEE if you want good branches as

• STRUCTURE
• TRANSPORT
• GEOTECH
• WATER RESOURCES
• ENVIRONMENT

You need to score 50–55+ for getting a call for written followed by Interview

And in IIT's as GUWAHATI, BHU, DHANBAD

You can get call at approx 45+ marks

Then if you are opting for EARTH Sciences , infrastructure or some interdisciplinary Branch then the lower score is also considered for Interview call.

Newer IIT's are few in number which offers M.tech in CIVIL department,

Patna is there among new where one can receive call for interview at 40–45+

Gandhinagar, HYDERABAD have a little bit higher cuttoff among the list of new IIT'S.

NOTE : This data is just an rough idea and it varies year by year , so I suggest you must apply for all institutes with sequence of your preferred branch

Even I had just mentioned the marks and not the score.