Based on the level of respect or formality, you can say "Could you take a picture of us, please?" in Korean in 3 ways:

• Informal: sajin jom jjik-eo jul-rae? (사진 좀 찍어 줄래?), sajin jom jjik-eo julsu itseo? (사진 좀 찍어줄 수 있어?), sajin jom jjik-eo julsu itni? (사진 좀 찍어줄 수 있니?)
• Formal: sajin jom jjik-eo jul-raeyo? (사진 좀 찍어 줄래요?), sajin jom jjik-eo julsu itseoyo? (사진 좀 찍어줄 수 있어요?), sajin jom jjik-eo julsu itseusipnigga? (사진 좀 찍어줄 수 있습니까?)
• Very Formal: sajin jom jjik-eo jusil-raeyo? (사진 좀 찍어 주실래요?), sajin jom jjik-eo julsilsu itseusipnigga? (사진 좀 찍어주실 수 있으십니까?)

- you (subjective): neo (너), neo-neun (너는), dangsin-eun (당신은), dansin-ggeseo-neun (당신께서는) - omitted here
- can do: hal su ittda (할 수 있다)
- to take a picture: sajin-eul jjikda (사진을 찍다)
- please: jom(좀), jebal (제발)

Please refer to How to pronounce Korean Alphabet for the English pronunciation in this answer.