Sir, my rank is 1046 and score is 677 with marks 59 in cse. What are the chances of getting into iits?

Hello Soni, first of all congratulations on getting a good score in GATE 2019. There are many factors that can determine your chances of getting into IITs. This year's cut off depends upon the parameters given below:
1. Total number of seats available in a college.
2. Reputation of that college and,
3. The previous year's cut off trends
4. If you are from the reserved or unreserved category.

So, following are the previous year's cut off patterns of the IITs, for Computer science and engineering:
1. IIT Delhi (2017)
Direct Admission- 900
Interview shortlisting
Gen- 790
OBC- 710
SC/ST/ PH - 550

2. IIT Madras (2018)
Gen- 770
Gen (PwD) - 283
OBC- 695
SC- 560
SC ( PwD) - 259
ST- 394

3. IIT Bombay (2018)
Gen- 750
OBC (NC) - 675
SC/ST - 500

4. IIT Kharagpur (2017)
Gen- 791
OBC- 681
SC- 590
ST- 418

5. IIT Guwahati (2017)
Gen- 770
OBC (NC) - 660
SC- 528

6. IIT Kanpur ( 2016)
Gen- 732
OBC- 665
SC- 567

7. IIT Roorkee
Gen- 56.34
OBC- 51.4
SC- 38.1
ST- 38.94

8. IIT Hyderabad (2017)
Gen- 731
OBC- 640
SC- 520
ST- 437

9. IIT Gandhinagar (2017)
Gen- 600
OBC - 540
SC/ST/PwD - 396

10. IISc Bangalore (2018)
Gen- 894
OBC- 806
SC- 632
ST- 509

11. IIT (ISM) Dhanbad (2017)
Gen- 571
OBC- 523
SC- 373
ST- 271

So according to the data I have provided, you can get admissions into IIT Gandhinagar and IIT Dhanbad if you are from general category. And you can give a try in all other IITs only if you are from the reserved category.

If you want to get a more accurate prediction of the Colleges you can get, please visit the College Predictor, link given below:
http://bit.ly/2J9S0MN

All the best!
I hope this helps.