Ratified treaties are published in the Government Gazette. The eGazette is published daily and is available on open access for 5 days - see current notices for newly ratified treaties. Access to older Gazettes requires a subscription to the Gazette Archive. We do not have a subscription.
The Singapore Treaties Database, maintained by the Attorney-General´s Chambers, contains records and the full text of bilateral and multilateral treaties to which Singapore is a party. Access to this database requires a subscription - we do not subscribe.
So the best place to find all bilateral and multilateral treaties is the UN Treaty Series Online - this contains all treaties deposited with the United Nations. You can search for a treaty, or see all Singaporean treaties by selecting 'Participant' from the top menu, then selecting 'Singapore' from the dropdown 'Filter' menu. Another participant can be added.
The treaties can be sorted by title, conclusion date, date of entry into force, and type (bilateral or multilateral).
Click on the 'See Details'; link of a treaty to see full treaty information, including the UNTS volume, if there is one.
On the details page, click the 'Text Document' or 'Volume in PDF' link to link to the full text official treaty.
The Constitution is silent on the incorporation of treaties domestic law. It is clear, however, that Singapore has a dualist system with respect to the domestic application of treaties. This means that treaties must be incorporated into the domestic laws of Singapore by the Legislature to have legal effect (Yong Vui Kong v Public Prosecutor  2 SLR 1129,  SGCA 11 – (Court of Appeal).
Source: The Singapore Legal System by Damien Chng and Jack Tsen-Ta Lee
Note: Yong Vui Kong v Public Prosecutor contains an extensive discussion of the domestic application of both treaties (paras 29, 40-53) and customary international law, in particular peremptory norms (paras 26-39 under the heading Jus Cogens).
For a detailed scholarly discussion of the relationship between international law and domestic law, see Siyuan Chen, 'The Relationship between International Law and Domestic Law: Yong Vui Kong v PP  3 SLR 489 [Case Note]' (2011) 23(1) Singapore Academy of Law Journal 350-366 (open access).
See also Singapore Law Watch's chapter on Singapore and International Law (open access), which provides a good overview of Singapore's engagement with international law making, with an emphasis on the work of the Singapore courts. This chapter includes a detailed section on treaty making and incorporation of treaties into domestic law, and judicial review of treaties that have been incorporated through domestic legislation, as well as judicial consideration of treaty obligations that have not been so incorporated. The chapter also considers the judicial approach to customary international law, noting 'Singapore courts have generally adhered to common law orthodoxy in approaching customary rules of international law; namely, that customary international law may be invoked in the Singapore courts as part of the common law'. Case law is referred to throughout this chapter.
Of the nine major human rights conventions, Singapore has ratified four: ICERD, CEDAW, CRPD, and CRC and one of its two Optional Protocols - OP-CRC-AC.
The Rule of Law in Armed Conflict (RULAC) Project website includes information on the international human rights and humanitarian treaties and regional treaties to which Vietnam is a party. This information includes relevant reservations, derogations and declarations. The website notes that 'Singapore is a party to relatively few human rights and humanitarian law treaties. It has not ratified the 1977 Additional Protocols to the Geneva Conventions or the 1998 Statute of the International Criminal Court'.
Please note that this website, whilst very useful, is somewhat dated and no longer updated. To check the current status of all human rights and related treaties to which Singapore is a party, use the official UN Treaties Series Online website (see box to the left for details).