Earning the right to ride in the trunk of someone's car. This is also the direct opposite of "riding bitch," where you are sitting center-backseat, sandwiched by your friends (aka: riding gay, riding whore) and also "riding shotgun," where you are sitting front passenger and live the good life. It is "trunk"'s responsibility for maintaining his own safety and accepting the fact that he may get hurt, while receiving additional personal space in situations where a small compact or sedan may have six or more total occupants. Complaining is assumed but is to be ignored by the driver in lieu of the verbal pact of the call.
Variations to "calling trunk" can include...well nothing, because normally it isn't an option and no one really fights for such a privilege as few have actually tried it to understand the advantages. Seniority rarely means anything when calling rifle.
Liza was riding rifle to chicken and rice because she didn't want to sit on Martin or Mike's lap as the 5th in the backseats..