Question: I made a game with Unity but the size of .apk file got so large, it is about 70mb...
Is there some way that I can compress my apk file?

Answer: 
Set your image size square and
Set unity suggested pixels.(32, 64, 128, 256, 512, 1024, 2048, 4096, 8192)
If your image size is 567x890 pixels then set this image in a 1024x1024 pixels background transparent blank image and save it as a png file.

Then in unity inspector set this image as a sprite and slice it by sprite editor. This process will make your image size reduce minimum 20%.

Example image and changes given below.

Before: resolution 567x890 pixel, size 1.9MB

After: resolution 1024x1024 pixel, size 1.3MB

Result: size 0.6MB reduced, almost 32%.

Image file Link: <https://drive.google.com/file/d/0B9zkzr6JdNYlaHhqcDVUSk9KNjA/view>
You can also choose to set the Device filter to Arm7. This will exclude certain devices, but I believe the number is quite small and it does minimize the apk size a bit. (This is located in Player Setting -> Other Settings -> Device Filter). You could try a build and see how much it would reduce it by and decide whether it was worth it.

Some Info on device filter: <http://answers.unity3d.com/questions/971648/device-filter-to-arm-7-only.html>