How to integrate an Android database in Drupal?
Consider using the Feeds module for such kinds of imports. Here is an excerpt from its project page:

Import or aggregate data as nodes, users, taxonomy terms or simple database records.

One-off imports and periodic aggregation of content
Import or aggregate RSS/Atom feeds
Import or aggregate CSV files
Import or aggregate OPML files
PubSubHubbub support
Create nodes, users, taxonomy terms or simple database records from import
Extensible to import any other kind of content
Granular mapping of input elements to Drupal content elements
Exportable configurations
Batched import for large files


Especially the first bullet seems to be what you're looking for.
Consider refining your question to provide some more details of the database format of your Android app. E.g. is it a PDO-compliant DBMS? If so, and in case you'd want to consider it, it might be possible to use a co-existance setup also (= use Drupal to only 'display' your data residing in your Android app).