Although most Android apps are originally written in Java, they are then converted into Dalvik code which runs on a Dalvik Virtual Machine on the Android device. Android devices don't natively have any Java Virtual Machine installed, and can't run Java apps or applets.
Someone would have to write a JVM that can run on Android and then make it available as a browser plugin (like Flash), or as part of a separate web browser. Both of these are options but I don't believe that anyone has written one yet, and searches of the Android Market don't show anything that's likely to help you yet.
If your Java app just was originally written for mobile devices and only uses the JavaME part of Java then it may be possible to convert it to run on Android using a technique like the one here Converting JavaME applications to the Android platform.
See also these previous questions:
- Are there any Android browsers that support loading a Java Applet in-browser?
- How can I install .jar files on my Android?