I want to buy an inverter for my house as there is a huge power cut and there is a lot of power fluctation and my question is can a inverter act s a voltage stablizer.
It depends on the duration and extent of the fluctuations. But doing so will likely kill your inverter under constant use. If you use a switch mode inverter with a wide range of voltage input, such that the input voltage range is higher than the maximal voltage fluctuations on your lines, then you can remove a lot of that noise. But this isn't the most effective way. Isolate electronics that really require a stable power source, and get a line conditioner for those, if you have to use one.
Electronics that have a switch mode power supply like most computers can deal with a large range of input voltage fluctuations, usually on a 120Vac line, this is from 90 to 130Vac. Other electronics like furnace motors, fans and so on are not as affected by these kinds of changes in voltage. Using switch mode power supplies on heavily fluctuating voltages that varies outside of the input voltage specifications of that power supply can quickly kill that power supply, or greatly reduce its life span.
Most consumer inverters are essentially switch mode power supplies, so if you use them outside of their range (if your power fluctuations constantly dip below or rise above the min and max allowed voltage inputs of your inverter), it will die quickly too.