Yes, you can. That being said, you can't play regulated online poker for real money in Texas. You'll either play at [1] sweepstakes poker sites or [2] offshore online poker rooms.

So to answer the question of can you make money playing poker, the answer is yes. However, you need to use a strong fundamentally sound poker strategy. This involves first picking the best games to play in. For a beginner I suggest low stakes full ring cash games online.