Is there a way to install RTC client into Rational Application Developer 9.6

Have you checked the existing posts? I believe p2 install is the only supported option.
https://jazz.net/forum/questions/236685/rtc-client-603-cant-be-installed-in-rsa-96-using-ibm-installation-manager
https://jazz.net/forum/questions/233247/rtc-602-in-rsa-96-installation-failed

I haven't tried for 9.6 but for me its working fine on 9.1  and i suppose that it should work for RAD 9.6 as well.

You can achieve this by 2 ways.
1.[RECOMMENDED] Just don't do any changes on RAD and directly install RTC Client 6.0.2 / 6.0.3 on your machine. When you open RAD you will see that RTC is integrated with RAD and you can confirm it from Jazz Administration Perspective in RAD.

2. Install P2 Eclipse extension for RTC in RAD Which should reflect in RAD as well.