Will moving my debt from one credit card to another affect my credit score?

In the FICO score formula, there are two different pieces of the credit utilization portion of the score: Overall utilization and Per-card utilization. By moving your debt from one card to the other, your overall utilization will stay the same, but your per-card utilization will go up (get worse). According to this article on NerdWallet, this will result in a hit to your credit score.

An important point to remember about the utilization portion of the credit score is that it has no memory. Each month, your current utilization is determined and used to calculate a new score. So as far as your mortgage is concerned, it only matters what your credit utilization is at the moment you are shopping for your mortgage.

Here is what I recommend: Instead of trying to save a few percentage points of interest and then worrying about your score, see how quickly you can pay off that $2900 debt. If you can do it over the next few months, both your overall and per-card utilization will be improved, and your score will rise. More importantly, your debt will be reduced and you'll be losing less money to the bank in interest each month. If you do this before you take out your mortgage, then it won't matter whether you moved the debt or kept it on your old card, because it will be gone.

Even better, I recommend doing what you can to pay off the entire debt on both cards as quick as you possibly can, preferably before buying your house. Develop a household budget that will ensure that you don't add to your credit card debt and can pay off the existing credit card debt as soon as possible.

It may go down slightly. While your total utilization will remain the same, one card will show almost 100% utilization (bad)

Here is what I (and Clark Howard) would suggest you do.

1. Transfer the balance. to the lowest APR card you have (your current plan).
2. Zero out to 14% card and STOP USING IT! Lock it away where you will not be tempted.
3. Pay down your 5% card as quickly as possible. This will raise your credit score by lowering your utilization ratio.