Can I increase my credit card limit by taking out a card securing my home?

Are you nuts? Why would you take out a secured credit card against your home? Why would you pledge your home as a security? If you want to raise your credit limit, then take steps to increase your credit score. Okay. Give focus on that.

Don't do that. manage your credit card responsibly. Don't cross the credit limit. Make the credit card payments in full. If you have credit card debts, then payoff them as early as possible.

It is a bad idea. Try to increase your income, and pay your balances in full every month before due date. Check your credit report for any negative information and try to remove it as soon as possible.
You might have requested for a credit limit raise. If your request isn’t approved this time, you'll receive an adverse action letter. Take note of the reason(s) listed in the letter. Improve your credit in those areas, wait a few months, and then try again.

If you've been a credit card for a long time, then you can request the credit card company/bank to increase your credit limit. Often talking face-to-face helps in such a situation.
Moreover, if your credit history is good, you can shop for other good credit card offers. Research well and decide on a card that's most suitable to you. if you get one, you can also let your present credit card company know that you've got a better offer from other bank.