A roller tappet for a fuel unit pump of an internal combustion engine is provided with a roller tappet bore for inserting the roller tappet within the internal combustion engine. The roller tappet includes a roller tappet body having a body longitudinal axis for connecting the roller tappet to a reciprocating element of the fuel unit pump. A cam roller contacts a cam lobe of a rotatable shaft of the internal combustion engine. The cam roller is rotatably mounted to the roller tappet body around a cam roller rotation axis. The external surface of the roller tappet body is configured to allow tilting of the roller tappet within the roller tappet bore for aligning the roller tappet with respect to the cam lobe of the rotatable shaft.