You can say 갈 거라서.

We usually say '내 친구가 집에 갈 거니까 나도 갈 거예요.'It is unsuitable here using'아/어 서'.

Hi Z,

I would want to say Because my friends are going home, I want to go home too.

Hence there is a 갈 거예요 for going home and 아/어 서 for because. But i am not sure i to join them together. 

Thanks

Your question needs clarification to ensure proper understanding. Presently you are leaving he reader to guess about the type of "joining" and that can have a very wide spectrum of possibilities.

Scientific: joining two types of molecules.

Social: Joining in marriage

And countless possibilities between the two I mentioned and more. So please try it again and use some additional words to express your thought.

Hope this helps.

Z