Maybe. Some inscriptions have been found on along the 'eastern route' to Byantium such as a rune stick in Staraya Ladoga (RyNLT2004;5) and the Berezan' Runestone in the Black Sea at the mouth of the Dniepr. But if there are any in Finland they've not been found yet. A Viking Age buckle was found in Tukkala in the 1980s (FiSAO1987;38) with the inscription "Bótvé, Hegvé owns me", but both the names and style are consistent with a Gutnish origin. So it's a lost or traded item.

A few runestones were reported in Vörå i Ostrobothnia in the mid-20th century but those were quickly (and unanimously) dismissed as modern by the experts. The only genuine stone inscription found in Finland is a mere fragment (FiNOR1998;14) found on the shore of Stora Ängesön in Hits/Hiittinen in 1998, about 30 km west-north-west of Hangö/Hanko. But the location makes it pretty unclear whether it was actually carved there, is some fragment of a more or was transported there serving as an anchor stone, or ballast stone, or fishnet weight, or some such.

There are no runic inscriptions on Åland either; despite that it was with all probability populated with Old Norse speakers in the Viking Age and is close to Uppland which has the highest density of stones by far. Yet at the same time, there are areas of Uppland with no stones, and neighboring regions like Dalarna with no stones, so the lack of stones in Åland isn't that astonishing in itself.

Since it was part of Sweden at the time, Finland was also subject to the first national surveys of runestones and 'antiquities' in the late 1600s, which cataloged many stones that've been lost since, but those didn't turn up anything either. (although it did lead to the first records of other significant things like the cult site at Levänluhta)

So in short there's just the one fragment, to date. So it'd be big news if a whole stone was found.