I've been looking around for a way to run a titan server in tomcat, but I can't find any information about this.
Anyone that knows how this can be done?
Since you are asking about running "Titan Server" in Tomcat, that really just means how to run Rexster inside of Tomcat. We dropped official support for Tomcat many, many versions ago, but I believe there are still those have it deployed that way which means it is in fact possible. I guess this would also only apply to hosting the Jersey-based REST endpoints and not RexPro.
To get started I would simplify the stack and just get Rexster running in Tomcat. I would search around the gremlin-users mailing list for what people have posted on the topic, but I think that this one is the most relevant:
https://groups.google.com/forum/#!msg/gremlin-users/s0g9Sd_xjSw/LQ3_ugL680cJ
If I remember correctly the key to making things work lies in this Rexster class: RexsterApplicationProvider. Note the class comments with the sample web.xml fragment.