Cronbach's Alpha should be applied only to unidimensional scales. If your scale is measuring three different sub-scales (factors), it is normal that the "global Alpha" is very low. I would calculate one Alpha for each different sub-scale. If the sub-scales are properly constructed, then the Alphas should be higher. You may consider to check the technical handbook of the scale, since it usually contains the reliability information. Then, you can compare the Alphas that they provide and the ones you have obtained.
If the Alphas you obtain for each sub-scale are still very low, you should consider using a different scale, or at least be aware of the lack of reliability of the assessment and notice it in your research communications. A low Alpha means that the items contained in a scale are not measuring the same construct, which may be a problem.
If you are further interested in this topic, you may also consider looking for the omega reliability index. Alpha index is by far the most popular reliability index, but it is known for making some assumptions that could not be realistic in some applied contexts (e.g., tau-equivalence). Omega index is more appropriate in these cases.
Thank you for giving a detailed view on the problem that I am going through. Yes it is a multidimensional scale and the sub scales' reliability also yield the low alpha score. I am quite disappointed over the output. The reliability outcome is seriously low. I need to check the scale's related handbook as you suggest to get some help. If it does not work then I may have to switch to another scale. Thank you once again.
I forgot to mention that if the sub-scales have inverse items, they should be recoded before computing Alpha.
You can also check the question "If Cronbach's alpha is low and I do not want to abandon my questionnaire, what needs to be done?". The answer of Karin Schermelleh-Engel is pretty good. I think this link should work and send you to this topic:
Ohk!!! That sounds interesting I will definitely check that too. I am feeling so low and demoralized, as the outcome is not upto expectation. This puts me into a complicated situation. Tough luck!! Let's see!!