Usually gate cutoff of 650 to 700 is required for entry into PhD programme in IIT.

But only that is not enough, you also need to qualify other criteria mentioned on their website. For example, iitk mentions the following: " An applicants with a bachelor's degree in engineering or science (4 year program) with a minimum of 75 percent marks/7.5 CPI with valid GATE/UGC/CSIR score required for financial assistance, except for graduates from IITs with a minimum CGPA of 8.0,

or
master's degree in science or an allied area, satisfying each of the following criteria:

(a) a minimum of 65 percent marks/6.5 CPI in the master's degree,

(b) first division in bachelor's degree, and

(c) JRF/CAT/GMAT/NET/95 percentile or higher in GATE."

Hence please be sure to check if you match the other criteria as well.