This happens because ASDM uses Swing which automatically tells Java that it is DPI aware.  
Java passes this information along to Windows, so Windows doesn't scale it.

If you are using Java 7 or before, you should be able to modify the arguments that are passed to Java to override Swing's DPI setting by modifying the following line at "%ProgramFiles(x86)%Cisco SystemsASDMrun.bat" from this:

javaw.exe -Xms64m -Xmx512m -Dsun.swing.enableImprovedDragGesture=true

To this:

javaw.exe -Xms64m -Xmx512m -Dsun.java2d.dpiaware=false -Dsun.swing.enableImprovedDragGesture=true

Unfortunately, Java 8 now has this setting hard-coded into the javaw.exe file itself, so this method will no longer work.  
Now you have to download something like Resource Tuner and modify the file itself. This is a good tutorial on how to modify it.