The paper you tried to link to didn't draw any connection between immigration and rape. The increased number of reported rapes in Sweden in the late nineties could be explained in a number of ways. One is that reporting increased thanks to increased awareness, another is legislative change, a third is revision of statistical routines. The two latter are mentioned in the paper.
Another thing that complicates a comparison:
"The Swedish data tend to lie at a higher level than that of the other countries (von Hofer, 2000). This is due to several factors: 1) in Sweden, a criminal offence is registered at the point that it is reported; 2) reported acts that later prove to be non-offences are not removed from the statistics; and, 3)
all offences listed on the same police report or committed on the same occasion (or in a series) appear as separate offences in Swedish statistics. Thus, the number of offences counted in Sweden is more comprehensive than in the other Nordic countries." (p. 7)