To analyze this claim, we consider ratings issued by conservative groups over the years. This will make it easy to spot any trend.
Of course, the usual caveats apply. These ratings are calculated based on a selection of votes. The votes rated each year are different, but these groups use fairly consistent standards that allow comparison over time.
First up is American Conservative Union (ACU), which has been rating Congress since the 1970s. Their ratings for Upton's entire tenure are graphed below.
A linear regression line is graphed along with the data. As you can see, the line is virtually flat, indicating no substantial change. There is actually a very slight decrease over time.
Upton's two best ratings occurred in 2002 and 2010, both of which were years when Upton received serious primary challenges from the right.
Many conservatives consider ACU's ratings too generous. More recently, several other organizations have begun their own ratings of Congress. FreedomWorks is a libertarian-leaning organization that has rated Congress since 2005.
Once again, the regression line is essentially flat. Upton's best year is also 2010.
Club for Growth is a free market organization that has also rated Congress since 2005.
Here we do see an upward trend, but Upton 2014 rating ties for his worst, so there isn't much reason to expect the trend to continue.
Some supporters of Upton will cite his endorsements by Right to Life in 2012 and 2014, after not having been endorsed in any previous years, as evidence of improvement. But this blog has documented Upton's long pro-abortion voting record in the past. He has not publicly renounced these votes, which leads to the suspicion that Right to Life's endorsement was based on political considerations.
In fairness, there is one major issue on which Upton's record actually has gotten better. Upton once had a very weak record on gun rights, with a 42% rating from the NRA in 2000. Since then, his ratings have improved. Upton usually votes the party line, but is not a leader on the issue.
Overall, though, Upton has not gotten any more conservative over the years. The claim to the contrary is false.