A phrase around "I give up" that is closest to sacrifice

A non profit organization is running a campaign that is encouraging people to sacrifice a small luxury and donate that money to a cause instead. They are building the campaign around Twitter hashtag #IGiveUp.

In general, I've seen "I give up" being used as "cease making an effort; admit defeat. (Google)".

Question: Is #IGiveUp an appropriate hashtag in this context? If not, any suggestions on what would be (Around #IGiveUp)?

You're quite right about the problem with #IGiveUp. It's kind of a clever pun (if intentional), but the problem is that "I give up" has such negative connotations — and is such a plausible hashtag on its own — that it overwhelms the cleverness.

As an alternative, I'd suggest #GiveItUpForACause. This is also a pun — "give it up for X" is a colloquialism meaning "please clap now for X" — but it has positive connotations, and it invites the reader to look deeper to see what is meant.

What are you going to give up for Lent

is a question Catholics commonly ask each other. Often it is something like chocolate or ice cream.

Thus the #IgiveUp is appropriate in your context. I give up will resonate with one billion Catholics and people who have Catholic friends. Giving the money spent daily on these treats to a charity will add up.

From Pope Francis’ Guide to Lent: What You Should Give Up This Year, by Christopher Hale (Feb. 2015)

“What are you giving up for Lent?” It’s a question a lot of people will get these next few days. If you want to change your body, perhaps alcohol and candy is the way to go. But if you want to change your heart, a harder fast is needed. This narrow road is gritty, but it isn’t sterile.