Sunscreen will reduce your ability to tan, but you absolutely still will get color. However, you are practicing much safer sun exposure when you wear sunblock, which should make it worth it to get a little bit less tan.
Can you get tan with sunscreen on?
Wearing a chemical- or physical-based sunscreen may help prevent the sun's rays from causing photoaging and skin cancer. It may still be possible to get a slight tan, even if you do wear sunscreen. However, no amount of deliberate tanning is considered safe.
Will I tan faster with sunscreen?
No matter whether you bask in the Sun all day or prefer to catch your rays over the course of the day, whilst doing other activities to gradually build up your summer glow, one thing's for sure: sunscreen is only there to keep you protected from skin damage, so it won't increase your tanning at all.