If you apply for a new balance transfer credit card, a hard inquiry will appear on your credit report. This will lower your credit score by a few points each time it occurs and will remain on your credit report for two years (although the negative impact will lessen over time).
On the other hand, having more available credit can decrease your total credit utilization ratio, which has the potential to improve your credit score. You can also improve your credit score as you make on-time payments on your credit and the total amount of debt you have decreases over time.