No it's not ethical. Your multinational software company most assuredly has a company policy regarding use of company and personnel data, such as phone numbers, as well as what type of behavior is considered appropriate. I suggest you first review that information before doing anything else.

Even if your company doesn't have any specific policy, this information has published by the company, explicitly for company and work-related use. Someone probably asked her to include her personal mobile number on the corporate database for reasons related to her job. That's the only capacity that number should be used, unless she gives you explicit permission to contact her. Like all the other employees, she is trusting that by sharing her personal data, it will not be misused.

now I am planning to introduce myself to her by means of sending texts.

Based on what I just wrote, this mostly likely against your company policy and could lead to you getting immediately fired. This is a clear misuse of her personal information, given that you do not work with her and your intentions of using this information is not related to your or her jobs. No one has asked you to contact her for work so you should not use this information to contact her for personal reasons.

As for your personal feelings about her... It's true that we cannot really help who we are attracted to, but your plans are very passive-aggressive and manipulative, and will not lead to any type of positive outcome. Respect her privacy. If you want to meet her, just walk over and say hello, or get a friend to introduce you. This isn't really the place for relationship advice, but if you cannot get over your fears of talking to her, you might want to find someone you feel more comfortable talking to — preferably someone you DON'T work with.

And if she says NO or she's not interested, respect that and leave her alone.