Yes, you are eligible to join Phd after MCA. To join Phd after MCA, You should have the MCA degree with a valid GATE score.

Procedure to join Ph.D after MCA
For admission in this course you need to appear in GATE Examination and secure valid GATE score for admission in Ph.D Score

PhD Duration
Minimum Duration: 2 Years
Maximum Duration: 5 Years

You can complete your Ph.D after MCA degree form following institutes
Symbiosis Institute Of Computer Studies & Research(SICSR), Pune,
Bengal Engineering and Science University(BESU), Kolkata
IGNOU
IIT Delhi
IISC Bangalore