Can we say delta% is significant if delta is significant? The question is simple. As for most of the online A/B test,  we are more interested in the delta% than delta, for example:
delta = (mean of treatment - mean of control)
delta% = (mean of treatment - mean of control)/mean of control. 

Let say if we use two-mean T-test, (statistics is Delta) we found the statistics Delta is significant. Then can we say delta% is significant?

*

*If yes, why?

*If not, in this case, then use delta% as statistics, how do we know its distribution (let's say the sample size is big)?

 A: Equivalent null hypotheses
Yes
When you are asking the question about significance then you relate to hypothesis testing.
For your situation, the hypotheses $H_0: \Delta = 0$ and $H_0: \Delta\% = 0$ are equivalent if you assume that 'mean of control' is non-zero (and if you do not assume that, then the $\Delta\%$ becomes a problematic definition due to the potential division by zero).
So if $\Delta$ is significantly different from $0$ then you can also claim that  $\Delta\%$ is significantly different from $0$.
Distribution of the data, not the parameter estimate
Also, note that the testing is normally not performed by observing only $\Delta$ or only $\Delta\%$. In that case, you would have a problematic situation with unknown nuisance parameters.
Instead, you use some test statistic which is based on the observations of treatment and observations of control, e.g their means $\mu_{treatment}$ and $\mu_{control}$. The test procedure would be the same for hypotheses $H_0: \Delta = 0$ and $H_0: \Delta\% = 0$ because you do not base yourself on the sample distributions of $\Delta$ or $\Delta\%$, but instead on the joint sample distribution of $\mu_{treatment}$ and $\mu_{control}$. You base a significance test on the data.
You might think that the significance test is different because estimates of $\Delta$ and $\Delta\%$ have different sample distributions. However, the parameter estimate and it's sample distribution is not necessarily the statistic that is used as a significance test.
For instance, when we perform linear regression, then we might estimate a parameter and perform a t-test which relates to the sample distribution of the parameter. But, we could also perform an analysis of variance and perform a F-test, which doesn't care how you express the parameter.
Significance testing is not primarily about the distribution of the estimate of some statistic (it can be used in testing, but it is derivative and not a first principle). Instead, it is in the first place about the distribution of the data conditional on the null hypothesis being true. The sample distribution of the data is the same for both null hypotheses. Therefore if an observation is significant for the one hypothesis, then it is also significant for the other.
Significance means that you made an extreme observation given the null hypothesis.

Confidence intervals
Where the use of $\Delta$ and $\Delta\%$ may differ is in the expression of confidence intervals. In this case, we are not talking anymore about the null hypothesis $H_0: \Delta = 0$ that assumes the parameter is equal to zero. But instead we consider the range of parameters $\theta$ for which the hypothesis $H_0: \Delta = \theta$ will pass a significance test (passing means no significance). The hypothesis $H_0: \Delta = \theta$ and $H_0: \Delta \% = \theta$, with $\theta \neq  0$ are not equivalent.
