The name is a contracted form of either Rosina or Gesina.
It was a common enough name in the 18th and 19th-centuries and even appeared in the U.S. top 1000 between 1880 and 1899. The highest it ranked within those years was in 1884 coming in as the 463rd most popular female name. This may have been due to a large influx of German immigrants at the time.
Currently, it is 75th most popular female name in Germany (2011).
The name could be a Germanized form of Sinya, a Russian diminutive of Euphrosyne. A more likely etymology is that it is from the German contraction of Gesina, the Frisian form of Gertrude, or it may be derived from the Frisian sin (sun). The name has also been sometimes correlated with a Bulgarian source, Sinia, (blue).
Currently, Sinja is the 456th most popular female name in Germany, (2011).
Other forms of the name include: