Yes and no. But the answer you're really looking for is no.
How does online roulette work?
When I say that the roulette wheel is fixed, I do not mean this in a way that will have an effect on your probability of winning at the table.
After you press the spin button, the casino software uses a Random Number Generator (RNG) to choose which number the ball is going to land on. So whilst it may appear as though the ball in spinning around and could land anywhere, the result of the spin has already been determined since pressing the spin button.
Here's an example RNG:
In spite of this, although the ball already has a set position for it to land in, the result is never determined based on where you have bet your chips. For example, just because you have bet on red, the software will never take this into consideration and think "I'm going to land on black and take their money".
The final result of the spin is always completely random, and it's just as random as any land casino. The only difference is that the ball knows exactly where it is going to land before the result is shown to you, and there is no physics involved like there is on a real table.
Note: The animation you see of the roulette wheel is for entertainment purposes only, but the final result was determined randomly.
Some people will always complain that something is rigged if the results do not go in their favor, so always take what sceptics have to say with a pinch of salt. I can understand though, because it's much easier to claim an online casino is rigged purely because of the fact that electronics and RNGs are involved, whereas it's harder to argue with the physics of a real-life table.
So I understand the temptation to declare that the wheel is fixed when you lose.
How do I know it's not rigged?
You don't have to take my word for it — you can test for yourself.
You can record the result of every spin of the wheel when you're playing. Once you have a few thousands spins under your belt you can check the results and see if they fall within a statistically likely range (see chi-squared). You'll want a large number of trials to be confident, but there's nothing stopping you from verifying the integrity of the results yourself.
For example, in 2011 someone found they were only winning 25% of their bets at an online craps table over 3,200 bets (when they should have been winning closer to 50%). It was later confirmed using statistical analysis that the software was indeed rigged.
So it's not impossible for casino software to be rigged. But what is very difficult is to get away with it when you have thousands of people playing the games every day. It's just too easy to spot anomalies.
I haven't heard of any other scandals taking place since, and I don't expect it to ever happen at the biggest online casinos.
The house already has the edge
At the end of the day, the house will always have the edge over players, and there is no need for them to extend this edge by rigging the results.
Whether a player decides to play craps, roulette, blackjack or any casino game, the house knows that they will be winning more money over the long run, and by rigging the games they are risking their entire business.
Tip: Stick with reputable casinos, because smaller fly-by-night operations have less to lose in terms of reputation.
Assuming you are playing at a respected casino, you should have no fear about the integrity of the results you are seeing. For what it's worth I trust the casinos I recommend on this site, as I have deposited and played at all of them for myself.
If I ever have anything to report though, I will let you know.